This book covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. An attempt has been made to formulate the various models fairly generally and to state the biological assumptions quite explicitly. The choice and treatment oftopics should enable the reader to understand and evaluate detailed analysesof many specific models and applications in the literature. The materialsuffices for a one-year course and is almost entirely self-contained. The little basic genetics needed for understanding it is presented in the text. Calculus and linear algebra are used freely. Previous exposure to elementary probability theory would be helpful. The major mathematical theme of the book is the dynamical analysis of recursion relations. Many exact and approximate techniques for investigating linear and nonlinear recursion relations in one dimension and in several dimensionsare developed and applied. The problems are an essential part of this book. Although some of them ask the reader merely to supply details of derivations in the text, many illuminate, rigorize, or extend these derivations. Some of the results in the problems are useful and important. They vary in difficulty; the harder ones offer a challenge even to good students.