Book List

Note: This list is going to be continuously updated (hopefully).



Calculus – Calculus by James Stewart

Linear Algebra – Linear Algebra Done Right by Sheldon Axler


General TopologyTopology: A Categorical Approach by Tai-Danae Bradley, Tyler Bradson and John Terilla

General Topology – Topology by James R. Munkres

Abstract Algebra – Algebra: Chapter 0 by Paolo Aluffi

Abstract Algebra – Algebra by Michael Artin

Abstract Algebra – Abstract Algebra by David S. Dummit and Richard M. Foote

Abstract Algebra – Algebra by Thomas W. Hungerford

Abstract Algebra – Basic Algebra by Nathan Jacobson

Real Analysis – Measure, Integration, and Real Analysis by Sheldon Axler

Real Analysis -Real Analysis: A Long Form Mathematics Textbook by Jay Cummings

Real Analysis – Real Analysis by Halsey Royden

Complex Analysis – Visual Complex Analysis by Tristram Needham

Complex Analysis – Complex Analysis by Lars Ahlfors


Commutative Algebra – Commutative Ring Theory by Hideyuki Matsumura

Algebraic TopologyAlgebraic Topology by Allen Hatcher

Algebraic TopologyA Concise Course in Algebraic Topology by J. P. May

Differential Geometry – Foundations of Differential Geometry by Shoshichi Kobayashi and Katsumi Nomizu

Differential Geometry – Differential Geometry: Bundles, Connections, Metrics and Curvature by Clifford Henry Taubes

Algebraic Geometry – Algebraic Geometry by Robin Hartshorne

Algebraic GeometryAlgebraic Geometry by Andreas Gathmann

Algebraic GeometryThe Rising Sea: Foundations of Algebraic Geometry by Ravi Vakil

Algebraic Geometry – Introduction to Algebraic Geometry by Brendan Hassett

Number Theory – A Friendly Introduction to Number Theory by Joseph H. Silverman

Number Theory – A Classical Introduction to Modern Number Theory by Kenneth Ireland and Michael Rosen

Number Theory – Algebraic Number Theory by J. W. S. Cassels and A. Frohlich

Number Theory – Algebraic Number Theory by Jurgen Neukirch


Elliptic Curves – The Arithmetic of Elliptic Curves by Joseph H. Silverman

Elliptic Curves – Advanced Topics in the Arithmetic of Elliptic Curves by Joseph H. Silverman

Modular Forms – A First Course in Modular Forms by Fred Diamond and Jerry Shurman

Etale CohomologyLectures on Etale Cohomology by J.S. Milne

Galois Cohomology – Cohomology of Number Fields by Jurgen Neukirch, Alexander Schmit, and Kay Wingberg

Langlands Program – An Introduction to the Langlands Program by Joseph Bernstein and Steve Gelbart


Number Theory – Fearless Symmetry: Exposing the Hidden Patterns of Numbers by Avner Ash and Robert Gross

Number Theory – Elliptic Tales: Curves, Counting, and Number Theory by Avner Ash and Robert Gross



Introductory Physics – Fundamentals of Physics by David Halliday and Robert Resnick


Classical Mechanics – Mechanics by Lev Landau and Evgeny Lifshitz

Electrodynamics – Introduction to Electrodynamics by David J. Griffiths

Quantum Mechanics – Introduction to Quantum Mechanics by David J. Griffiths

Statistical Mechanics – Thermal Physics by Charles Kittel and Herbert Kroemer


Quantum Field Theory – An Introduction to Quantum Field Theory by Michael E. Peskin and Daniel V. Schroder

Quantum Field Theory – Quantum Field Theory by Franz Mandl and Graham Shaw

General Relativity – Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll

Condensed Matter Physics – Solid State Physics by Neil W. Ashcroft and N. David Mermin


Astrophysics – An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A. Ostlie

Cosmology – Introduction to Cosmology by Barbara Ryden

String Theory – String Theory by Joseph Polchinski

String Theory – A First Course in String Theory by Barton Zwiebach

String TheoryJoe’s Little Book of String by Joseph Polchinski

Loop Quantum Gravity – Quantum Gravity by Carlo Rovelli

Loop Quantum Gravity – A First Course in Loop Quantum Gravity by Rodolfo Gambini and Jorge Pullin

Mathematical Physics – Geometry, Topology, and Physics by Mikio Nakahara

Mathematical Physics – Analysis, Manifolds, and Physics by Yvonne Choquet-Bruhat and Cecile DeWitt-Morette


Relativity – Relativity: The Special and General Theory by Albert Einstein

Other Book Lists Online:

Chicago Undergraduate Mathematics Bibliography

Chicago Undergraduate Physics Bibliography

A Physics Book List: Recommendations from the Net

Resources for Intro-Level Graduate Courses on Math3ma

E-Books, Lecture Notes, and Other Online Resources:

Mathematics Site – J.S. Milne

Jacob Lurie’s Home Page

Books on Terence Tao’s Blog