The lectures of Olof Leimar combined several topics of evolutionary game theory, life-history theory and population dynamics. In his first lecture he pointed out the differences between Darwinian fitness and invasion fitness, and how they are connected by means of demographic stability. The hawk-dove game served as a device to introduce evolutionary game theory and the notion of unbeatable strategies. The relation between game theory and adaptive dynamics was discussed. Symmetric and asymmetric games were presented, as well as repeated games. The sequential assessment game, a model of fighting behaviour, showed an application of evolutionary game theory. Invasion fitness was explained by means of the example of the problem of sex-ratio and reproductive value of Trivers and Willard. Finally, games with time-structure (in which players have the opportunity to react to each others behaviour) and reciprocity (a means to deal with variation in partner equality) were introduced as models that deal with social interactions.