How to Learn Physics for Free

A guide for the curious

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On this page I have gathered a list of free resources for learning physics. My intention is to cover the main areas of modern physics for the interested reader, stretching from Newton’s Laws to quantum field theory and beyond.

To really learn physics you should, of course, enroll in a university degree. But for those who are simply curious, or lack the time for full time studies, I hope that this guide will be of benefit. For those who do decide to study physics more seriously, it may also act as a companion; a set of resources to aid you in your study.

Introduction

Let’s open with a hard truth. Learning physics is difficult. The subject itself is vast; made up of dozens of barely related subfields. As a whole it is at times brutally mathematical, sometimes absurd and often disturbingly far from common sense.

In its essence, physics is an effort to understand the world around us. Its roots lie deep in human history; probably stretching back beyond the dawn of civilization to the time when humankind first began to question the world we live in. In both Babylonia and China the ancients observed the stars and planets, drawing out the first mathematical patterns in nature.

The Greeks, however, were the first to develop what we might call a “scientific” attitude to nature. Their experiments aimed to tease out the laws behind the world around us; and then to describe them in terms of numbers and geometry. Their conclusions were not always right, but they laid the foundation for a concept of science that flourished in Greece, and then in India and the Arab world.

Centuries later, Europeans once again engaged with those ancient ideas; an engagement that only grew as the Renaissance took place and new ideas swept through the continent. The scholars of that time - Copernicus, Galileo, Kepler and Newton among them - developed the scientific understanding of nature we now label physics: an understanding that opened the door to advances in gravitational theory, optics, thermodynamics and then, in the following century, to the wonders of the industrial revolution, electricity, mass communications and more.

The twentieth century, of course, saw a fundamental shift in physics. Einstein led the way, his theories of relativity forever reshaping our understanding of gravity, space and time. Quantum physics, following soon after, showed us a world more fundamental and bizarre than we could ever have imagined. This shift unlocked both wondrous and terrible things: we owe both the power of modern computing and the horrror of the atomic bomb to these discoveries.

Physics, then, is not just a dry subject of numbers and equations. It is a key part of our modern world; a subject that has given us a degree of mastery over the world around us; that opened the door to technologies that once would have seemed magical. It is also, when you penetrate its depths, deeply elegant and beautiful; a study not just of equations and laws but of how the cosmos itself is put together.

How to Use This Guide

Please don’t let the perceived difficulty of physics and maths put you off. Like anything else, these are subjects that can be learned, and can be done so by pretty much anybody. It may take time, it may be frustrating at times, it may occasionally go slower than you would like. But it can be done.

Below I have divided modern physics into its more or less accepted subdivisions. The biggest of these, of course, is the split between the “classical” physics of Newton, and the modern physics of Einstein and Quantum Theory. Within each are further sections: mechanics, thermodynamics and electromagnetism for classical physics, and quantum theory and relativity for modern physics.

For each I’ve provided links to free online textbooks and other resources. Where possible I have linked to material prepared by well-respected physicists, and I have tried to offer a range of options for each subject. If one is not working out for you, then feel free to abandon it and try a different book from another author.

The links also, however, range in difficulty and scope. The links in bold should be considered as “essential” material, that together is sufficient to give you a general understanding of physics. The rest is optional, but studying it will give you deeper insights into the topic.

You should, also, work through the material in roughly the order presented. Later textbooks will often assume knowledge taught before, and trying to leap into them too early will be more challenging than necessary. To get the best results you should also attempt to complete the problem sets included in many of the textbooks.

This list, of course, is incomplete. I have preferred online resources to off-line texts (though, of course, some “essential” texts are listed under General Resources). Over time I hope to expand it. Should you know of resources not listed here, please feel free to contact me. I will be grateful for your help.

General Resources

To begin, here are several good resources that provide a broad overview of physics. Many of these are also suitable for the more casual reader who is less ready or less interested in going deeper into sub-fields.

Similar Lists

• How to Become a Good Theoretical Physicist: A list of resources compiled by Gerard ‘t Hooft, winner of the 1999 Nobel Prize. Broad, with a focus on theoretical physics. Unfortunately it is not complete and several links no longer work.

• So You Want to Learn Physics…: A guide to learning physics from journalist and former physicist Susan Rigetti. A decent guide, but one more focused on purchasing physical textbooks than taking advantage of online resources.

• How to Learn Math and Physics: Another list of resources, this time from Joan Baez, a mathematical physicist at the University of California. Again, heavily based on textbooks, although links are provided where these are freely available online. As you might expect, Baez provides many resources on learning maths as well as physics.

The Feynman Lectures

• The Feynman Lectures: Collected in three volumes, Feynman’s lectures on physics make for an excellent starting point and later reference. Feynman, who was famously called “The Great Explainer”, covers his topics in an intuitive and easy-to-read manner.

Textbooks

As opposed to most other resources in this list, the three textbooks mentioned here are not freely available online. I have provided links to Amazon for each - note that these are affiliate links, and you can of course find these textbooks from other bookshops.

• University Physics with Modern Physics: By Young and Freedman, this is the standard undergraduate textbook for many courses in physics. Because of that you can often pick up a second hand copy.

• Mathematical Methods for Physics and Engineering: Again, a standard undergraduate textbook for university physics courses. This one focuses on the mathematics you’ll meet along the way.

• Course of Theoretical Physics: A legendary ten volume series by two Soviet physicists, Lev Landau and Evgeny Lifshitz. More advanced than University Physics, these textbooks are better suited for those readers looking for a deeper understanding and who already have completed the basics. For some reason Amazon omits volume V of the series, you can find it here.

Pre-Newtonian Physics

Pre-Newtonian physics (i.e., that of Ancient Greece, India and the Arab world) is rarely taught in universities today. Many of the ideas from this time are out of date, incomplete or just plain wrong. I include it here for those who are interested in understanding the path towards a more modern form of physics.

• Galileo and Einstein: Despite the title, this course traces our understanding of space, time and forces from Ancient Babylonia and Greece to the modern day, giving a nice overview of how our view of the physical world has changed over the centuries.

Mathematics

Mathematics lies at the heart of physics, and thus forms an essential prerequisite to going further. Here I have gathered material covering much of the maths key to later study. However, the field of mathematics related to physics is vast in its own right. Should you wish for more, see the further resources section below.

Fundamentals of Mathematics

The fundamentals are essential to all later subject areas. Make sure you are familiar with basic algebra, geometry, trigonometry as well as imaginary and complex numbers.

• Beginning Algebra: Tutorials on basic algebra provided by West Texas A&M University, covering the essentials from fractions to simple geometry.

• Intermediate Algebra: Continue the tutorials from West Texas A&M by moving onto linear equations, more complex fractions and roots.

• Dave’s Short Trig Course: Get a deeper look at trigonometry with this short course by David Joyce at Clark University.

• Dave’s Short Course on Complex Numbers: David Joyce continues with this quick introduction to imaginary and complex numbers.

• Linear Algebra: A free online textbook by Jim Hefferon, covering linear algebra as needed for a standard undergraduate course in physics.

Calculus

Calculus is the mathematics of continuously changing variables. It is what allows us to deal mathematically with velocities (changes in position), accelerations (changes in velocity) and other changing quantities. Historically it was developed by Leibniz and Newton, and is vital to understanding the problems addressed by Newtonian physics.

• Calculus Made Easy: An old textbook, but a good one that will give you a friendly introduction to calculus. 

• Calculus: From MIT, this free book will take you from basics of calculus through to partial derivatives and vector calculus. Working through it should give you the tools to go further into Newtonian physics.

• Notes on Differential Equations: After you grasp the essentials of calculus, this compilation of course notes will take you deeper into differential equations and their physical applications.

• Multivariable Calculus: This course gives an introduction to multivariable calculus from vectors to Gauss’ theorem. Much of this will have been covered by other resources already, but it is a useful summary of the topic and will find applications from mechanics to electromagnetism.

• Advanced Calculus: For a deeper view of calculus and its applications, this textbook provides an extensive overview of the subject. 

• Tools of Mathematical Physics: An introduction to mathematical techniques for physics. You should already be familiar with partial differential equations before starting this textbook.

• Mathematical Tools for Physics: After going through the above, this free online textbook will give you a good grounding in the general mathematics needed for physics.

Statistics

Lies, damn lies and statistics. People are famously bad at understanding statistics; studying it will help you critically evaluate many studies and experiments. It is also crucial to many fields of physics; especially so for thermodynamics.

• Concepts & Applications of Inferential Statistics: Don’t be afraid of the title: this resource is a friendly introduction to the statistical tools needed to do physics, especially of the experimental kind.

• Introduction to Probability: From Grinstead and Snell, this textbook takes you through the ideas and techniques of probability. To get the most of this book, you should already have some understanding of calculus, multiple integrals and matrices. 

Further Resources

Mathematics is an entire subject by itself, and extends far, far beyond what I have covered here. Rather than devote this page to maths, I suggest checking out the following resources for pointers on how to proceed.

• Mathematics for Theoretical Physics: An extensive online textbook covering the mathematics useful for pursuing and understanding theoretical physics. I recommend you to take a look, even if you just treat it as a reference.

• Basic Concepts of Mathematics: Despite the title, this book actually provides an introduction to a more rigorous study of mathematics than so far presented. Useful for going deeper into theory.

• How to Learn Math: Again from Baez, this list of resources provides a comprehensive path into the field of mathematics.

• Online Maths Books: Georgia Institute of Technology professor George Cain has collected this list of freely available online maths books. Unfortunately many of the links are out of date and no longer work.

Classical Physics

Classical physics was developed between the work of Newton in the 17th Century and that of Einstein in the 20th. Though today it has been superseded by quantum theory and relativity, classical physics is still relevant in describing much of the world that occurs at our scale - when, in other words, things are not too small and not too fast.

Mechanics

Classical mechanics begins with Newton’s famous laws of motion and deals with the movements of matter through space. It is a world of forces and accelerations; momentums and energies. Einstein’s theories have superseded it, though mechanics still remains relevant and mostly accurate when working with our everyday world.

• MIT OpenCourseware - Classical Mechanics: An online textbook and course provided through MIT OpenCourseware. It provides a solid introduction to classical mechanics.

• Newtonian Dynamics: This textbook covers classical mechanics from Newton’s Laws onwards, placing a particular focus on using them to describe the motions of planets and other objects in the Solar System. Worth going through to go a bit deeper into the main areas of classical mechanics.

• Classical Dynamics: From Cambridge University, David Tong provides these lecture notes on classical mechanics at an intermediate to advanced level.

• Graduate Classical Mechanics: A short online course covering advanced classical mechanics at a graduate level, written by Michael Fowler. A good mathematical background is essential here.

• Theoretical Mechanics: Another graduate level course on classical mechanics, this time from the Perimeter Institute.

Thermodynamics

The study of how heat moves. Its development helped us build and improve the steam engine; its consequences, spelt out in the fundamental laws of thermodynamics, predict the ultimate fate of life, the universe and everything. If you think you have built a perpetual motion machine, check here first.

“The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation.”

~ Arthur Eddington

• Thermal and Statistical Physics: By Harvey Gould and Jan Tabochnik, these book chapters, notes and problems cover the main concepts of thermodynamics. 

• Thermodynamics and Statistical Mechanics: This course by Richard Fitzpatrick introduces the ideas behind thermodynamics and statistical mechanics. Recommended reading to get a good overview of the subject. 

• Thermodynamics - Fundamentals and Application in Science: This online textbook introduces thermodynamics and then looks at its application to other areas of science, including biology and chemistry.

• Statistical Physics: An advanced level course on statistical physics from the Perimeter Institute.

• What is Entropy?: A short online book explaining the concept of entropy for non experts.

Electromagnetism and Optics

The mathematical description of electromagnetism was one of the crowning achievements of 19th Century physics. Maxwell’s Equations, first written down in 1861, showed how electricity and magnetism were intimately related; thus opening the door to mastery over those two forces. This, in turn, gave rise to some of the most transformative technologies of the 20th Century: electrical power, radio, television and radar.

• Optics: The field of optics was developed far earlier than other areas of electromagnetism and thus can be studied without much of the mathematics needed for the rest of the subject. These lecture notes offer a nice introduction to the topic.

• Electromagnetism and Optics: RIchard Fitzpatrick provides an introductory course into both electromagnetism and optics, covering the essential basics of the field.

• Classical Electromagnetism: Fitzpatrick goes deeper into electromagnetism in this course, beginning with Maxwell’s equations and ending with relativistic electromagnetism.

• Electromagnetism: A Cambridge University course on electromagnetism by David Tong. More intermediate level than beginner but worth following.

• MIT Electromagnetism: Lecture notes from an MIT course on electromagnetism. You should already have familiarity with Maxwell’s Equations before tackling this course.

• Electromagnetic Field Theory: An advanced textbook going deeper into the properties of electromagnetic fields and radiation phenomena.

The Rest of Classical Physics

Mechanics, thermodynamics and electromagnetism are the three primary branches of classical physics. Beyond that, however, classical physics includes many subfields that are either too specific or too advanced to cover above. Below I have collected some resources that fall into these categories:

• Solid State Physics: Solid state physics is the physics of materials, and particularly how electrons move through solids and how atoms arrange themselves into crystals and lattices.

• Lecture Notes in Fluid Mechanics: Fluid mechanics deals with the motion of liquids and gases, as opposed to solid objects. Technically a subfield of mechanics, but often taught as a separate course. These notes assume a knowledge of Newtonian mechanics.

• Fluid Mechanics: A second introductory course on fluid mechancis, this one from the University of Cambridge.

• Plasma Physics: Fitzpatrick provides an introduction to plasma physics and then to magnetohydrodynamics, the study of magnetic fluids. An essential topic to study if you are interested in nuclear fusion or the intricacies of stars though, truth be told, this subject is simply fascinating in its own right.

• Applications of Classical Physics: A textbook written by Nobel Prize winner Kip Thorne and astrophysicist Roger Blandford. This book covers much of classical physics, with the exception of mechanics, electromagnetism and basic thermodynamics. Both Thorne and Blandford are known for their work on black holes, so it should come as no surprise that the final chapters take the reader into the realm of general relativity.

• Richard Fitzpatrick’s Courses: I have linked to several of Fitzpatrick’s courses here. The rest, which do not easily fit into other sections, can be found here.

Relativity

Einstein’s revolutionary theories of relativity reshaped our view of the universe, forever changing the way we thought about time and space. His theory of special relativity arose from efforts to close contradictions in the laws of electromagnetics. General relativity, which came later, radically changed our conceptions of space and time.

Special Relativity

Einstein’s theory of special relativity tackles the motion of light throughout the cosmos. It was born out of an effort to resolve problems with Maxwell’s theory of electromagnetism, and ended with the abandonment of old ideas about time and space. Special relativity, discovered first, addresses the “special” case in which gravity can be ignored.

• Notes on Special Relativity: Michael Fowler introduces the ideas of special relativity in these lecture notes, starting from the experiments and theories that motivated its discovery.

• Special Relativity: Benjamin Crowell covers the theory of special relativity in this online textbook.

• Relativity: The Special and General Theory: Written by Einstein, this book introduces the theories of relativity from the master himself.

General Relativity

The theory of general relativity is one of the most elegant and beautiful ever written down. It speaks of a cosmos in which space and time are intimately linked; in which the presence of matter warps the fabric of both; and from which arises the phenomenon we perceive as gravity. Einstein’s work predicted many strange things, from black holes to wormholes, and reshaped our view of the universe.

• Lecture Notes on General Relativity: Sean M. Carroll provides this introductory course on general relativity. It makes for a decent starting point.

• Introduction to General Relativity: From Nobel Prize winner Gerald ‘t Hooft, these lecture notes provide a readable introduction to the topic of general relativity.

• General Relativity: An Introduction for Undergraduates: If neither of the other introductory courses worked for you, this brief introduction to general relativity may help.

• Cambridge General Relativity: Another course on general relativity, this time from David Tong.

• General Relativity: By Benjamin Crowell, this textbook covers the theory and geometry of general relativity. Problem sets with solutions are included.

• Light Rays, Singularities, and All That: From Edward Witten, this book takes a more advanced look at the implications of general relativity.

Quantum Theory

The quantum world is famously bizarre. Particles can vanish and reappear without warning, cross seemingly impenetrable barriers and somehow exist in two states at once. Even physicists are not immune to this strangeness - few, indeed, would claim to really understand what is happening in the quantum realm. Yet the mathematics works, and the theory provides, so far at least, our deepest understanding of nature.

Quantum Mechanics

Quantum mechanics provides the tools to describe the quantum world. These tools are heavy on mathematics and limited on conceptual understanding, but delving into them will give you a grasp of how things work in the quantum realm.

• UCSD Quantum Physics: From UCSD, these lecture notes provide a standard undergraduate level introduction to the subject of quantum mechanics.

• Quantum Mechanics: An alternative introduction to the subject, this time from Richard Fitzpatrick.

• Cambridge Quantum Mechanics: A first course on quantum mechanics, from David Tong at Cambridge Universtiy.

• Advanced Quantum Mechanics: A more advanced level course from Freeman Dyson. An old course, but still relevant.

• Classical and Quantum Mechanics via Lie Algebras: This book offers an alternative approach to both classical and quantum mechanics from an algebraic perspective. Certainly not useful as an introduction, though it may be of interest to those who wish to get a different mathematical view of quantum mechanics.

• Quantum Theory, Groups and Representations: Again going far beyond the essentials, this book approaches quantum theory from a mathematical perspective. Useful if you wish to gain a deeper understanding of the maths and symmetries behind quantum physics.

• Introduction to the Theory of Open Quantum Systems: A graduate level course on open quantum systems. Make sure you are comfortable with the basics of quantum mechanics before attempting this - though it is far from essential reading.

Particle Physics and the Standard Model

Our world is made from atoms; atoms are made of electrons, protons and neutrons; protons and neutrons are made from quarks. The standard model describes the subatomic world as we know it today, covering everything from quarks and electrons to neutrinos and the Higgs Boson, as well as the forces between them.

• Particle Physics: Based on lectures given at CERN summer schools, this course on particle physics is designed to be accessible to students with high school mathematics.

• Elementary Particle Physics: Lecture notes from the University of Rome introducing the subject of particle physics. A good starting point for the subject.

• Introduction to High Energy Physics: A second introduction to particle physics, though one that is slightly harder to follow than the course from Rome.

• Nuclear & Particle Physics: Another introduction to subatomic physics, beginning with the discovery of the electron, working through to the standard model and ending with an introduction to quantum field theory.

• The Standard Model: A Primer: A more advanced textbook introducing quantum field theory through the standard model of particle physics. 

Quantum Field Theory

The quantum field theory emerged in the 1920s and was largely developed by the 1960s and 70s. It describes particles in terms of underlying quantum fields, and combines classical field theory, special relativity and quantum mechanics. 

• Introduction to Quantum Field Theory: A solid introduction to quantum field theory, intended for final year undergraduates or early graduate students. 

• Quantum Field Theory: A textbook intended for newcomers to the field. The prerequisites are tough, so it may be advisable to revisit some of the material above if you run into difficulty.

• Quantum Field Theory by Sidney Coleman: Lecture notes from Coleman’s 1986 course at Harvard. Videos of his course are also available, though the quality is often rather poor.

• The Conceptual Basis of Quantum Field Theory: For those ready to take a deeper look at the Quantum Field Theory, Gerald ‘t Hooft reviews some of the conceptual issues with the theory.

• Quantum Field Theory I: From the Perimeter Institute, this online course introduces quantum field theory.

• Quantum Field Theory II: The Perimeter Institute goes deeper into quantum field theory in this follow-on course.

Beyond the Standard Model

Quantum theory, along with the Standard Model, is perhaps the most successful theory of physics ever conceived. Yet in one key area of physics - gravity - it is silent. We cannot, therefore, use it to tell us what happens inside a black hole, or in the earliest moments of the Big Bang. For that, physicists will need to move beyond the standard model, into the realm of quantum gravity, supersymmetry and strings. Be aware, much of what you will encounter here is highly speculative, theoretical and, above all, unproven.

• Quantum Gravity in Everyday Life: A short look at reconciling general relativity and quantum physics into a theory of quantum gravity.

• Supersymmetric Quantum Mechanics: A short course on supersymmetry by David Tong.

• Superspace: On supersymmetry. Once highly fashionable, today much less so - especially since the Large Hadron Collider failed to find any evidence to support it.

• Introduction to String Theory: String theory may be the future of physics, or it may be a load of unprovable nonsense. Gerald ‘t Hooft offers an introduction to the topic here.

• String Field Theory - A Modern Introduction: A second text introducing the ideas behind string theory.

• String Theory: From Cambridge University, David Tong provides this course for beginners in string theory.

Astronomy

So far I have focused on the key areas of physics. There are, of course, many branches and subfields of physics, each of which you can spend a lifetime studying in depth. Astronomy is perhaps the oldest of these, as the rhythms of the stars and planets were studied long before the Greeks dreamed up the foundations of what would later become physics. 

• Astronomy: A free textbook that covers much of our modern understanding of astronomy without a lot of mathematics. A good introduction for those looking for an overview of the subject.

• Observational Astronomy: These lecture notes cover the ways in which we actually observe the universe - from details of optics to the various kinds of detector used in modern observatories. Good reading for those interested in how we do astronomy.

• Introduction to Celestial Mechanics: Celestial mechanics concerns the movements of stars and planets, typically as seen from Earth. It is an ancient subject, once studied to divine messages from the Gods. Today it has found application in the orbits of satellites and spacecraft.

• The Fundamentals of Stellar Astrophysics: A slightly old textbook, but one that addresses our understanding of how stars burn and how they are structured.

• Principles of Heliophysics: Heliophysics covers the interaction between stars and planets. This textbook delves into how space weather affects planets, and how, in turn, that affects the potential for life on worlds across the galaxy.

• High Energy Cosmic Rays: Lecture notes on the origins and types of cosmic rays that bombard our planet from deep space.

Cosmology

Astronomy and astrophysics study the objects that fill the universe: the planets, the stars and the galaxies. Cosmology, by contrast, is the study of the universe itself - how it began, how it evolved, how it is shaped and, indeed, how it will all end. 

• Introduction to Cosmology: Lecture notes providing an introductory course on cosmology. It is useful to have at least some knowledge of general relativity before starting.

• TASI Lectures: Introduction to Cosmology: A somewhat more advanced “introduction” to cosmology. Requires a deeper understanding of general relativity to get the most from it.

• Cosmology: From the Perimeter Institute, this online course includes 64 lessons on cosmology.