Notes on Combinatorics

An upper-level introduction that moves from enumeration into graph theory and design theory. Its clear structure and worked examples make it a strong single reference for a full combinatorics course.

Joy Morris

A modern undergraduate introduction that pairs each chapter with linked videos and guided investigations. It covers counting problems, proof techniques, recurrences, generating functions, and graph theory.

Henry Adams, Kelly Emmrich, Maria Gillespie, Shannon Golden, Rachel Pries

A compact first course covering permutations, binomial coefficients, inclusion and exclusion, generating functions, and an entry into graph theory. A good pick for readers who want the essentials without extra length.

David Guichard

A comprehensive applied text spanning binomial coefficients, graph theory, partially ordered sets, generating functions, probability, and network flows. Its breadth makes it useful well beyond a first course.

Mitchel T. Keller, William T. Trotter

University lecture notes built around basic counting principles, the twelvefold way, and multinomial coefficients. Clear and example driven for a first pass through the subject.

Torsten Ueckerdt, Jonathan Rollin, Stefan Walzer