The field of mathematical biology or biomathematics rests on the interplay between mathematics and biology. The authors' position is clear, their main emphasis lies on the first; the book is written by mathematicians for mathematicians.
All through this textbook it is obvious that many of the topics dealt with are relevant research areas of at least one of the authors. The reader is led up to some of the most recent developments in the field. This book, addressing a wide range of interesting topics, is divided into seven parts, with in between a well-done interlude on replicator equations: Part 1. Selection dynamics and population genetics: a discrete introduction; Part 2. Growth rates and ecological models: an ABC on ODE; Part 3. Test tube evolution and hypercycles: a prebiotic primer; Part 4. Strategies and stability: an opening in game dynamics; Part 5. Compete, predate or cooperate: the struggle for permanence; Part 6. Back to the gene pool: gradients and cycles; Part 7. On sex and games: strategic and genetic evolution.
Mathematical results as well as powerful mathematical techniques and methods are worked out not in the usual definition-lemma-theorem-proof-corollary representation but via application in biological examples. As indicated in the introduction "$\ldots$many results are given in the form of exercises$\ldots$. Some of the exercises are quite hard, at least for one of the authors". Surely he is not the only one to have problems in cracking these exercises. Some of them might even lead to a diploma thesis. If these nuts are cracked, however, one has learned a lot. They are indeed challenging and hopefully many readers go through these special tasks.
The authors' hope "to point out some interesting sights along the way from undergraduate mathematics to current research" is successfully achieved. More than that, this outstanding work clearly represents biologically motivated mathematics interesting for graduate students in mathematics and biology coming to the subject for the first time, as well as for research workers in evolutionary theory.