Most of these notes were presented as part of a two-quarter course on theoretical population genetics at The University of Chicago. Almost all the students were either undergraduates in mathematics or graduate students in the biological sciences. The only prerequisites were calculus and matrices. As is done in these notes, biological background and additional mathematical techniques were covered when they were required. I have included the relevant problems assigned in the course. My aim in these notes is to formulate the various models fairly generally, making the biological assumptions quite explicit, and to perform the analyses relatively rigorously. I hope the choice and treatment of topics will enable the reader to understand and evaluate detailed analyses of specific models and applications in the literature. No attempt has been made to review the literature or to assign credit. Most of the references are to papers directly germane to the subjects and approaches covered here. Frequency of reference is not intended to reflect proportionate contribution. I am very grateful to Professor James F. Crow for helpful comments and to Mrs. Adelaide Jaffe for her excellent typing. I thank the National Science Foundation for its support (Grant No. DEB76-01550).