This book replaces our Theory of Evolution and Dynamical Systems, which was published in 1988 and has been reprinted several times. It now deserves to be put to rest.

The present text, which is totally restructured and contains a lot of new material, is no longer an interdisciplinary exploration but a tightly organized mathematical textbook on replicator dynamics and Lotka–Volterra equations.

Two important developments during the last decade have made it imperative to write this new book. Within the social sciences, game theory has gained a lot of ground; and within game theory, evolutionary and dynamical aspects have exploded. In our former book, it took us 150 pages of biological motivation to tentatively introduce the notion of a replicator equation. This is no longer warranted today: replicator dynamics is a firmly established subject, and it has grown so tremendously that our old volume definitely looks dated today.

It was exciting for us to see how many mathematical results obtained within the last decade could now be added to the curriculum. Of course, we had to economize elsewhere. This meant that the chapters on ecology, genetics and sociobiology which introduced the biological ideas underlying the mathematical models had to go. No regrets! All these aspects have been covered by one of us, in more readable form and for a general audience, in the Penguin book Games of Life.