This introduction to combinatorial analysis defines the subject as "the number of ways there are of doing some well-defined operation." Chapter 1 surveys that part of the theory of permutations and combinations associated with elementary algebra, which leads to the extended treatment of generating functions in Chapter 2. Chapter 3 considers the principle of inclusion and exclusion, which is indispensable to the enumeration of permutations with restricted position given in Chapters 7 and 8. Chapter 4 examines the enumeration of permutations in cyclic representation, while Chapter 5 surveys the theory of distributions and Chapter 6 considers partitions, compositions, and the enumeration of trees and linear graphs. Each chapter includes a problem section. Unabridged republication of the edition published by John Wiley & Sons, Inc., Canada, 1958.