In this book biological examples of Branching Processes are introduced from molecular and cellular biology as well as from the fields of human evolution and medicine and discussed in the context of the relevant mathematics, providing a useful introduction on how the modelling can be done and for what types of problems branching processes can be useful. As an aid to understanding specific examples, two introductory chapters provide background material in mathematics and biology. This book will interest scientists who work in quantitative modelling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, and cell and molecular biologists and bioinformaticians. The authors of this monograph are a mathematician and a cell biologist who have collaborated in the field of Branching Processes for more than a decade.