This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapterß1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey Theory. Chapterß2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, P'äoülya Theory, the stable marriage problem, and several important classes of numbers. Chapterß3 presents infinite pigeonhole principles, K"äoünig's Lemma, and Ramsey's Theorem, and discusses their connections to axiomatic set theory.

1 Graph Theory.- 2 Combinatorics.- 3 Infinite Combinatorics and Graphs.- References.