Branching processes are an important class of stochastic processes that models the growth of a population. They are widely used in biology and epidemiology to study the spread of infectious diseases and epidemics, and consist of a collection of independent random variables determining the number of children an individual will have. The subject has been actively developing since the pioneering works of Bienaymé, Galton and Watson.
The purpose of the talk is to introduce some basic ideas about these processes. We begin by defining the simple Galton--Watson process and its properties. Of particular interest in this field is the study of the extinction probability; in fact, these processes either explode or become extinct with probability 1. We also state some simple limit theorems. The second part of the talk focuses on multi-type branching processes, generalizing the previous model by allowing individuals to have different 'types' with different probabilistic behaviors. We can think of types as the different genetic traits of a population. We carefully define this new setting and describe the new version of the main properties and limit theorems.