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

##### Mathematics

**-Introductory-**

**Calculus** – Calculus by James Stewart

**Linear Algebra** – Linear Algebra Done Right by Sheldon Axler

**-Core-**

**General Topology** – Topology: 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

**-Advanced-**

**Commutative Algebra** – Commutative Ring Theory by Hideyuki Matsumura

**Algebraic Topology** – Algebraic Topology by Allen Hatcher

**Algebraic Topology** – A 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 Geometry** – Algebraic Geometry by Andreas Gathmann

**Algebraic Geometry** – The 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

**-Specialized-**

**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 Cohomology** – Lectures 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

–**Popular**–

**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

##### Physics

**-Introductory-**

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

**-Core-**

**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

**-Advanced-**

**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

**-Specialized-**

**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 Theory** – Joe’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

–**Popular**–

**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