Abstract: Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and allows for new phenomena, in particular the dynamical emergence through evolutionary branching of two or more coexisting lineages employing different strategies/traits from a single initial ancestral population. In this talk, I will introduce the basic concepts and show how they are used in practice through example. If time allows, I will also discuss how evolutionary game theory can be understood from the perspective of adaptive dynamics.