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Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result. Table of Contents Introduction Part I: Basics 1 Fundamental Coefficients 2 Formal Series and Infinite Matrices Part II: Methods 3 Generating Functions 4 Hypergeometric Summation 5 Sieve Methods 6 Enumeration of Patterns Part III: Topics 7 The Catalan Connection 8 Symmetric Functions 9 Counting Polynomials 10 Models from Statistical Physics Solutions to Selected Exercises Notation Index