Some Mathematical Models from Population Genetics : École dÉté de Probabilités de Saint Flour XXXIX 2009 This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some like the classical Wright Fisher model date right back to the origins of the subject. Others like the multiple merger coalescents or the spatial Lambda Fleming Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained the models are carefully motivated and tools for their study are presented systematically.