Combinatorial theory is a fascinating branch of mathematics with numerous applications in engineering, the physical sciences, the social sciences, economics, and operations research. This is an introductory book on the subject. It is an outgrowth of a set of class notes I used in teaching a course in applied combinatorial mathematics offered by the Electrical Engineering Department at the Massachusetts Institute of Technology.
The topics covered may be divided into four groups which are representative of the various aspects of applied combinatorial mathematics: enumerative analysis (Chapters 1 to 5), theory of graphs (Chapters 6 to 9), optimization techniques (Chapters 10 to 13), and design of experiments (Chapter 14). The level of presentation is appropriate for advanced undergraduate and first-year graduate students. No prior knowledge of combinatorial mathematics or modern algebra is assumed. Sections marked with * may be omitted without loss of continuity. Necessary algebraic concepts are introduced as needed, and those sections marked with • may be skipped by the student who has had a course in modern algebra.
In view of the fact that this is an introductory text, I did not attempt to compile an extensive bibliography. Rather, it is hoped that the student will make more effective use of a small number of selected references accompanying each chapter.
An integral part of the book is the collection of problems at the end of each chapter. Some of these problems require the student to apply the abstract concepts developed in the text, whereas others require him to extend these concepts in a natural way. A book containing the solutions to all problems has been prepared.

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