Originally evolved in the 19th century from an attempt by Galton and Watson (earlier work of Bienaymé has been found recently) to show how probability related to the extinction of family names, the theory of branching processes has become widely used as a theoretical basis for the study of populations of such objects as genes, neutrons, or cosmic rays. The present hardcover volume, originally sponsored by The RAND Corporation, was the first systematic and comprehensive treatment of a theory of mathematical models for the development of populations whose members reproduce and die, subject to laws of change. Beginning with the classical Galton-Watson model for the propagation of a family of objects all of one type, the author then extends the theory of objects of several types and to objects described by continuous variables. He next applies the theory to one of the simpler mathematical models for neutron chain reactions. Succeeding chapters treat Markov branching processes with a continuous time parameter and age-dependent branching processes. The last chapter gives the mathematical theory of electron-photo cascades, one of the components of cosmic radiation.