This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy-Weinberg law, the Lotka-Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject.