Counting Rocks! An Introduction to 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 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

An accessible text that starts from the Fibonacci numbers and builds toward generating functions, distributions, and the pigeonhole principle. Well suited to readers who want intuition alongside the formulas.

Carl G. Wagner