This paper is concerned with the statistical approach to population genetics. The genetical characteristics of the population under consideration are the population size and the gene frequencies.

The limitations on the population are (a) the individuals are either all haploids or all diploids; (b) the alleles are only two in number, either A or a; (c) there are no selection and migration pressures occurring in the population.

Three main model types, the branching processes, the Markov chains, and the diffusion processes are discussed.

Published results on the subject are presented along with some new investigations. Comparable results obtained by various authors are checked, some of which are found to be invalid.

Continuous approximations are used to derive some of the results of discrete processes, but a chapter is devoted to the justification of such approximations.