This book is the first of a two-volume basic introduction to enumerative combinatorics at a level suitable for graduate students and research mathematicians. It concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. The book covers those parts of enumerative combinatorics of greatest applicability to other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods (including the Principle of Inclusion-Exclusion), partially ordered sets, and rational generating functions. There are a large number of exercises, almost all with solutions, which greatly augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

Review of the hardback:‘Stanley’s book is very readable and a mine of information.’

E. Keith Lloyd Source: Journal of the LMS

‘This book is already a classic … a most instructive text, which is sheer delight to read and study. I am looking forward to the publication of the long awaited Enumerative Combinatorics, Vol. II.’

C. Krattenthaler