This book provides an introduction to the main concepts of combinatorics, features fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise questions and observations within the field. The Second Edition contains over fifty new examples that illustrate important combinatorial concepts and methods that range in level from routine (i.e. special kinds of sets, functions, and sequences) to advanced (i.e. the SET game, the Gitterpunktproblem, and enumeration of partial orders).  The tables and references have been updated throughout, reflecting advances in Ramsey numbers and Thomas Hales' solution of Kepler's conjecture).  In addition, many exciting new computer programs and exercises have been incorporated to help readers understand and apply combinatorial techniques and ideas.  This new edition has made it possible for readers to encode and execute programs for formulas that were previously inaccessible, allowing for a deeper, investigative study of combinatorics.  The book is divided into three sections - Existence, Enumeration, and Construction all of which begin with a simply stated first principle that is then developed step-by-step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice.  Many important combinatorial methods are revisited and repeated several times throughout the book in exercises, examples, theorems, and proofs alike, enabling readers to build confidence and reinforce their understanding of complex material.