"Preface: Since its inception in the 1960s, evolutionary game theory has become increasingly influential in the modelling of biology, both in terms of mathematical developments and especially in the range of applications. Important biological phenomena, such as the fact that the sex ratio of so many species is close to a half, the evolution of cooperative behaviour and the existence of costly ornaments like the peacock's tail, have been explained using ideas underpinned by game theoretical modelling. The key concept in biological games is the Evolutionarily Stable Strategy (ESS), which resists invasion by all others once it has achieved dominance in the population. This static concept is very powerful, and is the focus of analysis of the majority of models, and while we discuss numerous other mathematical concepts, this is the most important one for our book. For a number of years the authors have been aware that, while there are a number of good books on evolutionary games, a particular type of book that we were looking for did not exist. The catalyst for writing this book was a discussion between Nick Britton and MB on the subject of books in evolutionary game theory. Nick was looking for a book on this subject for the Taylor and Francis Mathematical and Computational Biology book series. After discussing this, the authors decided that this was an opportunity to write the book we had been looking for. The book that we were missing was a wide ranging book covering the major topics of evolutionary game theory, containing both the more abstract mathematical models and a range of mathematical models of real biological situations, and this is the book we have tried to write"--