General mathematics books open the door to the ideas behind every other branch of math. This collection brings together free PDF titles, from first principles to formal proofs.
You will find titles on number theory, discrete mathematics, and mathematical analysis. There are also practice workbooks and exam prep for school, GED, and beyond.
Many titles come from university scholars like Oscar Levin and Elias Zakon. Download any general mathematics book in PDF now, with no signup and instant access.
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Foundations
General Mathematics Books
Broad, foundational titles that introduce the discipline and the logic of mathematical proof. These books suit anyone building a strong base before specializing.
Broad lecture notes spanning linear algebra, differential equations, and calculus. A compact reference for undergraduates who want core topics gathered in one place.
A transition-to-proof textbook built around logic, sets, proofs, functions, and relations. Designed to bridge calculus and upper-level abstract mathematics.
A problem-driven tour of mathematical thinking, using carefully chosen elementary problems to reveal the depth behind familiar topics. Rewards curiosity over rote technique.
An accessible introduction to the language of proof and abstract mathematics, covering logic, sets, functions, and relations. A solid foundation for proof-based courses.
A wide-ranging introduction to contemporary mathematics for general readers, exploring patterns, infinity, and reasoning. Emphasizes ideas and beauty over heavy machinery.
A practical mathematics course built in modules, from order of operations and fractions to measurement, geometry, and formulas. Aimed at applied and technical learners.
Graduate-level notes on mathematical methods for engineers and scientists, covering multivariable calculus, linear algebra, and differential equations. Strong on applied technique.
A seventh-grade practice workbook with worksheets on fractions, decimals, percents, equations, and geometry. Structured lessons with skills checks for steady progress.
An advanced secondary-level textbook reaching into geometry, number theory, series, and inequalities. Written for capstone and competition-bound students.
Concise lecture notes on number theory covering divisibility, primes, modular arithmetic, and classic theorems by Fermat, Euler, and Wilson. A clear, exercise-driven entry point.
A comprehensive introduction to number theory covering divisibility, congruences, multiplicative functions, primitive roots, and quadratic residues. Clear proofs and exercises make it suitable for self-study.
A widely used open introduction to discrete mathematics, with counting, graph theory, logic, and proofs. Inquiry-based exercises make it ideal for a first course in the subject.
An open textbook on combinatorics and discrete structures, from counting techniques and generating functions to graphs, posets, and network flows. Strong on applied problem solving.
A rigorous introduction to real analysis covering sequences, limits, continuity, and differentiation. Built on clear definitions and full proofs for students moving into proof-based mathematics.
Beatriz Lafferriere, Gerardo Lafferriere, Nguyen Mau Nam
A classic, self-contained treatment of mathematical analysis covering set theory, metric spaces, sequences, and continuity. Known for its careful, fully proved exposition.
An exploratory linear algebra textbook covering vectors, matrices, and linear transformations through guided problems. Includes code and a hands-on approach to the subject.
