This book fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The text first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the book discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. The second edition adds a new chapter on analytic combinatorics, new sections on advanced applications of generating functions, and new exercises to all chapters.

Miklos Bona received his Ph.D in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bona has mentored numerous graduate and undergraduate students. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an editor-in-chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.

Basic methods. Applications of basic methods. Generating functions. Counting permutations. Counting graphs. Extremal combinatorics. Analytic combinatorics. Symmetric structures. Sequences in combinatorics. Counting magic squares and magic cubes. Appendix: The method of mathematical induction.