This text introduces current evolutionary game theory where ideas from evolutionary biology and rationalistic economics meet - emphasizing the links between static and dynamic approaches and non-cooperative game theory. Much of the text is devoted to the key concepts of evolutionary stability and replicator dynamics. The former highlights the role of mutations and the latter the mechanisms of selection. Moreover, set-valued static and dynamic stability concepts, as well as processes of social evolution, are discussed. Separate background chapters are devoted to non-cooperative game theory and the theory of ordinary differential equations. There are examples throughout as well as individual chapter summaries. Because evolutionary game theory is a fast-moving field that is itself branching out and rapidly evolving, the author has focused on clarifying and explaining core elements of the theory in an up-to-date, comprehensive and self-contained treatment. The result is a text for second-year graduate students in economic theory, other social sciences and evolutionary biology. The book should also serve as an introduction for those embarking on research in this area as well as a reference for those already familiar with the field. Jorgen Weibull provides an overview of the developments that have taken place in this branch of game theory, discusses the mathematical tools needed to understand the area, describes both the motivation and intuition for the concepts involved and explains why and how it is relevant to economics.