This book covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. I have tried to formulate the various models fairly generally and to state the biological as­ sumptions quite explicitly. I hope the choice and treatment of topics will en­ able the reader to understand and evaluate detailed analyses of many specific models and applications in the literature. Models in population genetics are highly idealized, often even over­ idealized, and their connection with observation is frequently remote. Further­ more, it is not practicable to measure the parameters and variables in these models with high accuracy. These regrettable circumstances amply justify the use of appropriate, lucid, and rigorous approximations in the analysis of our models, and such approximations are often illuminating even when exact solu­ tions are available. However, our empirical and theoretical limitations justify neither opaque, incomplete formulations nor unconvincing, inadequate analy­ ses, for these may produce uninterpretable, misleading, or erroneous results. Intuition is a principal source of ideas for the construction and investigation of models, but it can replace neither clear formulation nor careful analysis. Fisher (1930; 1958, pp. x, 23-24, 38) not only espoused similar ideas, but he recognized also that our concepts of intuition and rigor must evolve in time. The book is neither a review of the literature nor a compendium of results. The material is almost entirely self-contained. The first eight chapters are a thoroughly revised and greatly extended version of my published lecture notes (Nagylaki, 1977a).