Stochastic population dynamics studies the evolution of a given population in time under the effect of randomness.

The aim this talk is to introduce to this subject by first considering the case where the source of randomness is purely demographic, i.e. it comes only from birth and death events, and then continue our exposition by adding extra sources of randomness, such as competition pressure or the effect of the environment.

Some recent developments to this subject will be provided, in particular about the long term behaviour of such models such as the probability of extinction or stability of the population.