Ulf Dieckmann started his lectures by mentioning the dichotomies of the notion of fitness, a central concept in evolutionary thinking. After a discussion on evolutionary game theory and its shortcomings, he set out to enunciate the theory of adaptive dynamics: a theory of phenotypic evolution that goes beyond classical game theory. Evolutionary replicator dynamics were introduced as one of the origins for the theory of adaptive dynamics. Several stochastic and deterministic models of adaptive dynamics were derived, together with their relations. Furthermore pairwise invadibility plots as tools to conclude whether or not phenotypes can coexist, were introduced. In his last session Ulf Dieckmann discussed the various time-scales (on the level of resident population dynamics, mutation processes, adaptation and branching) that play a role in evolutionary processes.