Here I’ve listed and described my favorite physics texts by topic. See here for my favorite maths texts. For each of the books listed below, I either own it or have used it in a course. I’ll also mark each with a symbol to indicate the difficulty (I) for introductory, (M) for intermediate, and (A) for advanced.

### Basic Physics

##### Feynman - *The Feynman Lectures* (I)

The classic undergraduate three-volume set written by physics' greatest elucidator.

##### Tipler - *Physics* (I)

More modern, all-encompasing volume for introductory physics courses.

##### Ohanian - *Modern Physics* (I)

Common reference for first courses in special relativity.

##### Taylor - *Introduction to Error Analysis* (I)

Standard introductory reference for experimental methodology, statistical analysis of data, and error propagation.

### Classical Mechanics

##### Taylor -*Classical Mechanics* (I)

Great undergraduate reference text, usually seen in an upper-division undergraduate mechanics course.

##### Thornton, Marion - *Classical Dynamics* (M)

Undergraduate level classical mechanics text, more advanced than Taylor.

##### Goldstein - *Classical Mechanics* (A)

The standard graduate-level text on mechanics.

##### Arnold - *Mathematical Methods of Classical Mechanics* (A)

Mathematical tools for classical mechanics. Notation is a bit old (and Russian), for instance $[A, B]$ is used for the vector cross product instead of $A \times B$.

##### Libermann, Marle - *Symplectic Geometry and Analytical Mechanics* (A)

Excellent reprint of a text that analyses the symplectic structure of classical mechanics. Insofar as classical mechanics is truly geometry of phase space - this text presents a rigorous treatment of symplectic forms, spaces, and how they relate to Hamiltonian systems. Very rigorous.

### Electricity & Magnetism

##### Griffiths - *Introduction to Electrodynamics* (I)

Standard undergraduate level text on E&M, frequently used for upper-division courses on electricity and magnetism. Interestingly, doesn’t include much on circuits.

##### Jackson - *Classical Electrodynamics* (A)

The standard graduate text on E&M, a rite of passage.

##### Baylis - *Electrodynamics: A Modern Geometric Approach* (A)

Interesting advanced text that analyses the geometric implications of EM theory, including deriving the Minkowski metric from the Clifford algebra. Draws really nice connections between special relativity and Maxwell’s equations.

##### Hehl - *Foundations of Classical Electrodynamics* (A)

Excellent advanced reference on the detailed mathematical structure of electromagnetic theory, including exterior algebras and metric-free examination of Maxwell-Lorentz spacetime relations. Strong emphasis placed on axiomatic approach, considerable rigor.

##### Scheck - *Classical Field Theory: On Electrodynamics, Non-Abelian Gauge Theories and Gravitation* (A)

Interesting advanced text that analyses Maxwell’s equations as an example of a gauge theory, then develops generalized notions of gauge theory. Considers applications to gravity along the lines Weyl considered in the early days of GR.

### Classical Gravity (GR)

##### Carroll - *Spacetime and Geometry* (I)

Clean, modern reference that is relatively self-contained. Builds the essential differential geometry (quickly) before introducing gravitational concepts. Notation is very close to modern mathematical literature.

##### Schutz - *A First Course In General Relativity* (I)

Less modern introductory text to GR, worth reading after / with Carroll.

##### Wald - *General Relativity* (M)

Standard graduate level introduction to GR. Excellent exposition of mathematical aspects of GR with a medium amount of rigor. Does not discuss bundles, and only briefly mentions tetrads.

##### Poisson - *Gravity* (M)

Moderately advanced text covering details of Newtonian, Post-Newtonian approximation methods.

##### Poisson - *A Relativist’s Toolkit* (A)

Advanced techniques for applying GR to astrophysical situations, assumes a working knowledge of GR.

##### Misner, Thornton, Wheeler (MTW) - *Gravitation* (A)

Standard reference text, absolutely massive. Includes the most detail on the most topics out of any book on the subject, and is a useful reference for practitioners.

##### Straumann - *General Relativity* (A)

Great supplement reference at the graduate level. Shows full derivations of Schwarzschild and Kerr metrics, has great discussion on black hole thermodynamics. Also includes material of Cartan structure of the field equations and affine connections.

##### Geroch - *General Relativity: 1972 Lecture Notes* (A)

Geroch is a master. These lecture notes, while brief, expertly weave the mathematics and physics from a spacetime-first perspective using a wealth of visuals. Geroch shows how physical phenomena can be explained first in spacetime, then decomposed into space + time to recover familiar quantities.

##### Chandrasekhar - *The Mathematical Theory of Black Holes* (A)

One of the most rigorous treatises on black holes in existence, with pages upon pages of calculations. Excellent introduction to tetrad formalism as well as Newman-Penrose formalism. Covers basically any topic in black holes imaginable, including derivations / construction of Schwarzschild, Reissner-Nordstrom, and Kerr solutions, perturbations and effect on electromagnetic phenomena.

### Numerical Relativity (NR)

##### Baumgarte - *Numerical Relativity* (M)

Clean, modern introduction to NR, briefly reviews GR but most focus is on numerical considerations.

##### Alcubierre - *Introduction to 3 + 1 Numerical Relativity* (A)

Standard, in-depth reference on numerical relativity.

### Quantum Gravity (QG)

##### Baez - *Gauge Fields, Knots, and Gravity* (I)

If you can read one introductory book on gravity, make it this book. Baez has the unique ability to present enough detail to give the interested reader a foothold in related mathematical subjects while staying high-level enough to provide a coherent overview of the many related fields that appear in quantum gravity. Introduces vector field functional formalism, gauge fields and relations to local symmetries, elements of knot theory including crossings and windings, and how these apply to (loop) quantum gravity.

##### Pullin - *A First Course in Loop Quantum Gravity* (I)

A friendly introduction to LQG that doesn’t assume prior familiarity with either GR or QFT. While this book doesn’t go into a great deal of depth, it provides a concise, high-level view of what loop quantum gravity is and how it fits into the landscape of theoretical physics.

##### Rovelli - *Covariant Loop Quantum Gravity* (M)

A high-level text that introduces more detailed structure than the text above; however, this is mostly a summary for new researchers in the field that have some familiarity with LQG. Carlo’s inimitable style makes this an enjoyable read.

##### Rovelli - *Quantum Gravity* (M)

Graduate level text on loop quantum gravity; the starting point for any serious reading into LQG. Jumps pretty quickly past the GR essentials and into the tetrad formalism, introduces the concept of spin networks, intertwiners.

##### Ashtekar - *Lectures on Non-Perturbative Canonical Gravity* (M)

Excellent set of lecture notes from the eponymous discoverer of the spinorial formulation of GR. These are a must-have for any LQG reader.

##### Thiemann - *Modern Canonical Quantum General Relativity* (A)

The rigorous complement to Rovelli, a monolithic volume of mathematical detail. Discusses details of spaces of connections, bundle structures, and other aspects of the mathematical details of LQG.

##### Gambini, Pullin - *Loops, Knots, Gauge Theories and Quantum Gravity* (A)

Excellent, detailed reference for loop representations with applications to gauge theories and lattice techniques. Discusses applications to gravity including braid theories. Predates Rovelli and Thiemann, so final chapter is mostly interesting for understanding development of the current theory.

### Mathematical Physics

##### Jeevanjee - *An Introduction to Tensors and Group Theory for Physicists* (I)

Excellent introduction to the theory of groups and tensors, aimed at physics students. Self contained, Jeevanjee (properly) introduces tensors as multilinear maps, and derives all the familiar behavior including transformation “rules” and index mechanics. Introduces key concepts from Lie theory with just-enough rigor to prepare reader for further study, includes many examples from physics including SU(2), SO(3) and others. Introduces representations in a clear way as well. Cannot recommend highly enough.

##### Isham - *Modern Differential Geometry for Physicists* (I)

The lecture notes of a course taught by a renowned expert in quantum gravity on the mathematical preliminaries for classical gravity. Includes the standard intro to differential geometry; however, Isham also includes an excellent exposition of connections and bundles (which is usually missing from such texts). Isham also includes multiple perspectives on elementary definitions, unifying the various methods by which these concepts are conventionally introduced.

##### Arfken - *Mathematical Methods for Physicists* (I)

Standard reference text at the undergraduate level for mathematical methods. Has many examples of each technique introduced, but doesn’t introduce certain topics from the graduate level such as integral regularization.

##### Balakrishnan - *Mathematical Physics: Applications and Problems* (M)

Graduate level reference on mathematical methods from a renowned author of mathematical physics books. Goes into more depth than Arfken (as expected), including functional analysis, operators and algebras. Covers distributional derivatives.

##### Rudolph, Schmidt - *Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems* (A)

Great, verbose reference for differential geometry and applications to physics. The first part covers manifolds and elementary lie theory with applications to Lagrangian mechanics.

##### Rudolph, Schmidt - *Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields* (A)

Second volume of a great reference on differential geometry, covering aspects that are often missing from gravitation texts including fiber and principal bundles, Clifford algebras and spin geometry, and gauge theory.

### Quantum Mechanics

##### Griffiths - *Introduction to Quantum Mechanics* (I)

Ubiquitous undergraduate text on quantum mechanics, covering the standard sequence of “shutup and calculate” quantum mechanics. Wavefunctions, some (unfortunately Copenhagen) interpretation, simple potentials, and basic properties of quantum systems. New edition has a chapter about symmetries and conserved quantities, a nice introduction to Noethers theorem.

##### Cohen-Tannoudjhi - *Quantum Mechanics* (M)

Three volume series at the graduate level on all aspects of quantum mechanics. Incredibly thorough, Cohen shows details that are omitted from most other quantum mechanics texts. The many supplemental chapters work through examples that bring a higher degree of clarity to QM topics. Volumes I and II cover standard graduate level quantum mechanics, formalism and simple potentials, angular momentum and algebraic implications,

##### Shankar - *Principles of Quantum Mechanics* (M)

Intermediate reference text on the mathematical aspects of quantum mechanics. Still focused largely on particle-based non-relativistic systems. More rigorous references included in “Quantum Theory” section below.

##### Feynman and Hibbs - *Quantum Mechanics and Path Integrals* (A)

Accessible introduction to the path integral formulation of quantum mechanics from the inimitable Feynman (who created the path integral approach).

##### Sakurai - *Modern Quantum Mechanics* (A)

Included for completeness, a standard graduate-level text. Much more terse than Cohen. The author only wrote the first three chapters, then the rest of the text was written posthumously from lecture notes by collaborators - I include this detail because it explains why the first three chapters are the best in the book - formalism, dynamics, and angular momentum. The remaining material I would recommend sourcing elsewhere.

### Quantum Field Theory (QFT)

##### Zee - *Quantum Field Theory in a Nutshell* (M)

Approachable introduction in a relaxed style, Zee provides a clear presentation of QFT essentials.

##### Peskin, Shroeder - *An Introduction to Quantum Field Theory* (M)

The standard, graduate level reference used in QFT courses.

##### DeWitt - *The Global Approach to Quantum Field Theory* (A)

Insightful two-volume set taking a unique approach to developing QFT.

##### Weinberg - *The Quantum Theory of Fields* (A)

Standard rigorous reference on QFT.

##### Coleman - *Lectures of Sidney Coleman on Quantum Field Theory* (A)

Set of advanced lectures from a renowned elucidator of QFT.

### Quantum Theory - eg. Foundations, Formalism

##### Norsen - *Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory* (I)

Accessible introduction to a field often omitted from the standard physics education - interpreting quantum theory. Norsen presents the main interpretations, Copenhagen, Many Worlds, Bohmian, Spontaneous Collapse. Excellently introduces ontological considerations as well as the measurement problem.

##### Woit - *Quantum Theory, Groups and Representations: An Introduction* (A)

Rigorous, unconventional approach to developing quantum theory. Woit eschews the standard approach of introducing classical systems first, then ‘quantising’ these systems with bad analogies. Instead, Woit develops intuition around the algebraic nature of quantum theory using examples that have no classical analogues. Excellent text with unique perspective.

##### Hall - *Quantum Theory for Mathematicians* (A)

Rigorous introduction to quantum theory aimed at mathematicians, using a Hilbert-space approach. Covers the role of Lie theory in quantum mechanics as well as a more rigorous presentation of path integrals.

##### Landsman - *Foundations of Quantum Theory: From Classical Concepts to Operator Algebras* (A)

Detailed (read: thick) exposition of operator algebras and the connection to classical Poisson structures.

### Statistical Mechanics & Thermodynamics

I’ve not found a thermo book that included everything satisfactorily, but below are some that I’ve used in various courses.

##### Schroeder - *Introduction to Thermal Physics* (I)

Standard undergraduate thermodynamics book.

##### Kardar - *Statistical Physics of Particles* (M)

Clear, concise statistical mechanics and thermodynamics book at the graduate level. Derives the laws of thermodynamics in an abstract setting, includes several unique derivations (some are probably worth skipping).

##### Kardar - *Statistical Physics of Fields* (A)

Follow up volume to the one above, excellent discussion of Landau principles.

##### Balakishnan - *Elements of Nonequilibrium Statistical Mechanics* (M)

Great reference on nonequilibrium systems and their statistical properties.

##### Berlinsky, Harris - *Statistical Mechanics: An Introductory Graduate Course* (A)

Graduate level text focusing on more mathematical aspects of thermodynamics and statistical mechanics, including the renormalization group, Landau theory and mean field theory. Many examples considered including superconductivity and quantum fluids.