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
Theories and Theorems 