  Many socio-economic and biological processes can be modeled as systems of
interacting individuals. The behaviour of such systems can be often described
within game-theoretic models. In these lecture notes, we introduce fundamental
concepts of evolutionary game theory and review basic properties of
deterministic replicator dynamics and stochastic dynamics of finite
populations. We discuss stability of equilibria in deterministic dynamics with
migration, time-delay, and in stochastic dynamics of well-mixed populations and
spatial games with local interactions. We analyze the dependence of the
long-run behaviour of a population on various parameters such as the time
delay, the noise level, and the size of the population.
