The first part of this book is a simple introduction to ecological modelling, aiming mostly at explaining the dynamical aspects (long-term behaviour, equilibria, basins of attraction, regular and irregular oscillations etc.).

The second part is a concise course in the dynamics of evolutionary game theory. We start out with the notion of evolutionary stability, and go on to explore the underlying field of replicator dynamics, which is based on the assumption that strategies spawn copies of themselves in proportion to their average payoff. The success of this approach should not make one forget, however, that there are other ways that strategies can spread, based on learning, for instance, or alternative mechanisms. We have emphasized the wide range of such alternative models in our chapters on adaptive dynamics, best-reply dynamics and imitation dynamics.

In the third part of the book, we concentrate on Lotka–Volterra equations and replicator dynamics and study them in parallel, stressing the special aspects of these dynamical systems, for instance the occurrence of heteroclinic attractors. But we keep the main population dynamical motivation firmly in the foreground, emphasizing notions like permanence and saturated equilibria.

In the last part, we return to the original reason for introducing game dynamics. It was intended at first as a shortcut to understanding frequencydependent genetics. We deal with dynamical systems in classical genetics describing selection, mutation, recombination and differential fertility, and proceed to address the basic issue which motivated Maynard Smith: how will mutants introducing new behavioural strategies fare under selection?