The favorable reception of our book and its use for a variety of courses on combinatorial mathematics at numerous colleges and universities has encouraged us to prepare this second edition. We have added new material and have updated references for this version. A number of typographical and other errors have been corrected. We had to change “this century” to “the last century” in several places.

The new material has, for the most part, been inserted into the chapters with the same titles as in the first edition. An exception is that the material of the later chapters on graph theory has been reorganized into four chapters rather than two. The added material includes, for example, discussion of the Lovàsz sieve, associative block designs, and list colorings of graphs.

Many new problems have been added, and we hope that this last change, in particular, will increase the value of the book as a text. We have decided not to attempt to indicate in the book the level of difficulty of the various problems, but remark again that this can vary greatly. The difficulty will often depend on the experience and background of the reader, and an instructor will need to decide which exercises are appropriate for his or her students. We like the idea of stating problems at the point in the text where they are most relevant, but have also added some problems at the end of the chapters. It is not true that the problems appearing later are necessarily more difficult than those at the beginning of a chapter.