Here I’ve listed and described my favorite maths texts by topic. See here for my favorite physics 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.

Algebra

Dummit and Foote Abstract Algebra (I)

Hungerford Algebra (M)

Lang Algebra (A)

Mac Lane Categories for the Working Mathematician (M)

Pinter A Book of Abstract Algebra (I)

Calculus

Marsden Vector Calculus (M)

Spivak Calculus (I)

Stewart Calculus Early Transcendentals (I)

Combinatorics

Diestel Graph Theory (M)

Harris Combinatorics and Graph Theory (I)

Differential Equations

Evans Partial Differential Equations (A)

Haberman Applied Partial Differential Equations (M)

Strauss Partial Differential Equations (M)

Sundaram A First Course in Optimization Theory (I)

Geometry

Do Carmo Differential Geometry of Curves and Surfaces (I)

Lee Introduction to Smooth Manifolds (A)

Lee Introduction to Riemannian Manifolds (A)

Ratcliffe Foundations of Hyperbolic Manifolds (A)

Spivak Differential Geometry (M)

Tu Differential Geometry (M)

Linear Algebra

Axler Linear Algebra Done Right (I)

Das Tensors (M)

Grinfeld Introduction to Tensor Analysis (I)

Lang Linear Algebra (M)

Rentlen Manifolds, Tensors, and Forms (M)

Roman Advanced Linear Algebra (A)

Probability & Statistics

Buhlmann Statistics for High-Dimensional Data (A)

Brzezniak Basic Stochastic Processes (I)

Casella Statistical Inference (A)

De Veaux Stats: Data and Models (I)

Durrett Probability: Theory and Examples (A)

Halmos Measure Theory (M)

Ross A First Course in Probability (M)

Representation Theory

Fulton Representation Theory (A)

Hall Lie Groups, Lie Algebras, and Representations (M)

Topology

Crossley Essential Topology (I)

Edelsbrunner and Harer Computational Topology (M)

Ghrist Elementary Applied Topology (M)

Hatcher Algebraic Topology (M)

Lee Introduction to Topological Manifolds (A)

Munkres Topology (M)