this talk will provide a brief introduction to mathematical population genetics, focusing on coalescent theory. we will introduce the classical wright-fisher population model and explain why, in this model, the genealogy of the population can be described by kingman's coalescent, in which each pair of ancestral lineages merges into a single lineage at rate one. we will then derive some consequences of this model. at the end of the talk, we will discuss some recent research related to models of populations with large family sizes.