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Textbook recommendations

This is a list of textbook recommendations for studying mathematics and theoretical physics.

✋ Disclaimer:

• 📚 most textbooks on the list are graduate level textbooks (many of them are better be read with some prior knowledge of subjects in question)
• ⚛️ the list is made for people who are studying mathematics and theoretical physics, so the recommended textbooks will probably be too mathematical and abstract for people intrested in other STEM fields
• 🥗 textbooks selection describes my personal taste and does not imply any objective judgement on how one should study physics and mathematics

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Physics

1 Classical Mechanics

1. Goldstein, "Classical Mechanics"
2. Landau and Lifshitz, "Mechanics"
3. Arnold, "Mathematical Methods of Classical Mechanics"
4. Spivak, "Physics for Mathematicians, Mechanics"
5. Bonus memes:
   • Takhtajan, "Quantum Mechanics for Mathematicians" (Ch. 1)
   • Marsden and Ratiu, "Introduction To Mechanics And Symmetry"
   • Abraham and Mardsen, "Foundations of Mechanics"
   • Thirring, "Classical Mathematical Physics" (Part I)
   • Kubiznak, "Classical Mechanics" (Video)
   • Osborne, "Symplectic Geometry and Classical Mechanics" (Video)

2 Special Relativity

1. Carroll, "Spacetime and Geometry" (Ch. 1)
2. Landau and Lifshitz, "The Classical Theory Of Fields" (Ch. 1–2)
3. Bonus memes:
   • Lightman, Press, Price, and Teukolsky, "Problem Book in Relativity and Gravitation" (Ch. 1–3)
   • Misner, Thorne, and Wheeler, "Gravitation" (Ch. 1–2, 5–6)

3 Electrodynamics

1. Landau and Lifshitz, "The Classical Theory Of Fields" (Ch. 3–9)
2. Misner, Thorne, and Wheeler, "Gravitation" (Ch. 3–5)
3. Jackson, "Classical Electrodynamics"

4 Quantum Mechanics

1. Shankar, "Principles of Quantum Mechanics"
2. Sakurai and Napolitano, "Modern Quantum Mechanics"
3. Townsend, "A Modern Approach to Quantum Mechanics"
4. Takhtajan, "Quantum Mechanics for Mathematicians"
5. Bonus memes:
   • Woit, "Quantum Theory, Groups and Representations"
   • Cohen-Tannoudji, Diu, and Laloe, "Quantum Mechanics"
   • Weinberg, "Lectures on Quantum Mechanics"
   • Thirring, "Quantum Mathematical Physics" (Part I)
   • Faddeev and Yakubovskii, "Lectures on Quantum Mechanics for Mathematics Students"
   • Fock, "Fundamentals of Quantum Mechanics"
   • Landau and Lifshitz, "Quantum Mechanics"

5 Statistical Mechanics

1. Pathria, "Statistical Mechanics"
2. Kardar, "Statistical Physics of Particles"
3. Landau and Lifshitz, "Statistical Physics (Part 1)"
4. Landau and Lifshitz, "Physical Kinetics"

6 General Relativity

1. Carroll, "Spacetime and Geometry"
2. Wald, "General Relativity"
3. Hobson, Efstathiou, and Lasenby, "General Relativity: An Introduction for Physicists"
4. Bonus memes:
   • Lightman, Press, Price, and Teukolsky, "Problem Book in Relativity and Gravitation"
   • d'Inverno, "Introducing Einstein's relativity"
   • Misner, Thorne, and Wheeler, "Gravitation"
   • Landau and Lifshitz, "The Classical Theory Of Fields" (Ch. 10–14)
   • Hawking and Ellis, "The Large Scale Structure of Spacetime"
   • Chandrasekhar, "The Mathematical Theory of Black Holes"

7 Quantum Field Theory

0. Rubakov, "Classical Theory of Gauge Fields"
1. Ryder, "Quantum Field Theory"
2. Peskin and Schroeder, "An Introduction to Quantum Field Theory"
3. Itzykson and Zuber, "Quantum Field Theory"
4. Bonus memes:
   • Lancaster, "Quantum Field Theory for the Gifted Amateur"
   • Weinberg, "The Quantum Theory of Fields"

8 Cosmology and Astrophysics

1. Weinberg, "Lectures on Astrophysics"
2. Weinberg, "Cosmology"
3. Rubakov and Gorbunov, "Introduction to the Theory of the Early Universe"
4. Morison, "Introduction to Astronomy and Cosmology"
5. Page, "The Little Book of Cosmology"

9 Introductory physics

1. Halliday, Resnick, and Walker, "Fundamentals of Physics"
2. Weinberg, "Foundations of Modern Physics"
3. Bonus memes:
   • Knight, "Physics for Scientists and Engineers"
   • Young and Freedman, "University Physics with Modern Physics"
   • Giancoli, "Physics"
   • Knight, Jones, and Field, "College Physics"
   • Serway and Vuille, "College Physics"

10 Mathematics for Physics

General courses

• Cahill, "Physical Mathematics"
• Szekeres, "A Course in Modern Mathematical Physics"
• Byron and Fuller, "Mathematics of Classical and Quantum Physics"
• Hassani, "Mathematical Physics"
• Arfken, Harris, and Weber, "Mathematical Methods for Physicists"
• Riley, Hobson, and Bence, "Mathematical Methods for Physics and Engineering"

Groups and algebras

• Robinson, "Symmetry and the Standard model"
• Georgi, "Lie Algebras in Particle Physics"
• Gilmore, "Lie Groups, Physics and Geometry"
• Isaev and Rubakov, "Theory of Groups and Symmetries"
• Neumaier and Westra, "Classical and Quantum Mechanics via Lie Algebras"
• Elliott and Dawber, "Symmetry in Physics"

Geometry

• Novikov and Taimanov, "Modern Geometric Structures and Fields"
• Wasserman, "Tensors and Manifolds with Applications to Physics"
• Schutz, "Geometrical Methods of Mathematical Physics"
• Nakahara, "Geometry, Topology and Physics"
• Nash and Sen, "Topology and Geometry for Physicists"
• Frankel, "The Geometry of Physics"
• Choquet-Bruhat and DeWitt-Morette, "Analysis, Manifolds and Physics"
• Doran and Lasenby, "Geometric Algebra for Physicists"

11 Handbooks (physics)

• Benenson, Harris, Stocker, and Lutz, "Handbook of Physics"
• Menzel, "Fundamental Formulas of Physics"
• Polyanin and Chernoutsan, "A Concise Handbook of Mathematics, Physics, and Engineering Sciences"
• Woan, "The Cambridge Handbook of Physics Formulas"

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Mathematics

1 Real Analysis

1. Zorich, "Mathematical Analysis"
2. Abbott, "Understanding Analysis"
3. Wade, "Introduction to Analysis"
4. Bonus memes:
   • Apostol, "Mathematical Analysis"
   • Folland, "Real Analysis: Modern Techniques and Their Applications"
   • Axler, "Measure, Integration and Real Analysis"
   • Rudin, "Real and Complex Analysis"

2 Complex Analysis

1. Ahlfors, "Complex Analysis"
2. Shabat, "Introduction to Complex Analysis"
3. Lang, "Complex Analysis"
4. Freitag and Busam, "Complex Analysis"
5. Needham, "Visual Complex Analysis"
6. Bonus memes:
   • Shakarchi, "Problems and Solutions for Complex Analysis"
   • Remmert, "Theory of Complex Functions"
   • Brown and Churchill, "Complex Variables and Applications"
   • Stein and Shakarchi, "Complex Analysis"

3 Ordinary Differential Equations

1. Arnold, "Ordinary Differential Equations"
2. Boyce, DiPrima, and Meade, "Elementary Differential Equations and Boundary Value Problems"
3. Adkins and Davidson, "Ordinary Differential Equations"
4. Coddington, "An introduction to Ordinary Differential Equations"
5. Tenenbaum and Pollard, "Ordinary Differential Equations"

4 Mathematical Physics

General courses

• Szekeres, "A Course in Modern Mathematical Physics"
• Cahill, "Physical Mathematics"
• Byron and Fuller, "Mathematics of Classical and Quantum Physics"
• Hassani, "Mathematical Physics"
• Hassani, "Mathematical Methods for Students of Physics and Related Fields"
• Arfken, Harris, and Weber, "Mathematical Methods for Physicists"
• Richtmyer, "Principles of Advanced Mathematical Physics"

Calculus of Variations

• Gelfand and Fomin, "Calculus of Variations"
• Chang, "Lecture Notes On Calculus Of Variations"
• Ewing, "Calculus of Variations with Applications"
• Rindler, "Calculus of Variations"

Partial Differential Equations

• Evans, "Partial Differential Equations"
• Olver, "Introduction to Partial Differential Equations"
• Strauss, "Partial Differential Equations: an Introduction"

Integral Equations

• Wazwaz, "A First Course in Integral Equations"
• Zemyan, "The Classical Theory of Integral Equations"
• Tricomi, "Integral Equations"

Functional Analysis

• Kreyszig, "Introductory Functional Analysis with Applications"
• Brezis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations"
• Duistermaat and Kolk, "Distributions: Theory and Applications"
• Kanwal, "Generalized Functions: Theory and Applications"
• Strichartz, "A Guide to Distribution Theory and Fourier Transforms"

5 Probability Theory

Basic

• Rozanov, "Probability Theory: A Concise Course"
• Ash, "Basic Probability Theory"
• Anderson, Seppäläinen, and Valkó, "Introduction to Probability"
• Ross, "A First Course in Probability"
• Bertsekas and Tsitsiklis, "Introduction to Probability"
• Parzen, "Modern Probability Theory and its Applications"

Advanced

• Rosenthal, "A First Look at Rigorous Probability Theory"
• Williams, "Probability with Martingales"
• Resnick, "A Probability Path"
• Kallenberg, "Foundations of Modern Probability"

6 Linear Algebra

1. Axler, "Linear Algebra Done Right"
2. Kostrikin and Manin, "Linear Algebra and Geometry"

7 Algebra

1. Dummit and Foote, "Abstract Algebra"

8 Analysis on manifolds

1. Spivak, "Calculus On Manifolds"
2. Warner, "Foundations of Differentiable Manifolds and Lie Groups"
3. Flanders, "Differential Forms with Applications to the Physical Sciences"

9 Differential Geometry and Topology

1. Novikov and Taimanov, "Modern Geometric Structures And Fields"
2. Nakahara, "Geometry, Topology and Physics" (Ch. 2, 5, 7)
3. Schutz, "Geometrical Methods of Mathematical Physics"
4. Bonus memes:
   • Kobayashi and Nomizu, "Foundations of Differential Geometry"
   • Gadea, Masque, and Mykytyuk, "Analysis and Algebra on Differentiable Manifolds (Workbook)"

10 Handbooks (mathematics)

• Bronshtein, and Semendyayev, "Handbook of Mathematics"
• Gradshtein, and Ryzhik, "Table of Integrals, Series, and Products"
• Olver, Lozier, Boisvert, and Clark, "NIST Handbook of Mathematical Functions"
• Jeffrey and Dai, "Handbook of Mathematical Formulas and Integrals"
• Korn and Korn, "Mathematical Handbook for Scientists and Engineers"
• Lipschutz, Spiegel, and Liu, "Mathematical Handbook of Formulas and Tables"
• Abramowitz and Stegun, "Handbook of Mathematical Functions"
• Polyanin and Zaitsev, "Handbook of Ordinary Differential Equations"
• Polyanin and Nazaikinskii, "Handbook of Linear Partial Differential Equations"
• Polyanin and Zaitsev, "Handbook of Nonlinear Partial Differential Equations"
• Polyanin and Manzhirov, "Handbook of Integral Equations"