There is nothing wrong with or incorrect about this book. The problem is that the information could be presented much more effectively and in fact is elsewhere!

If you're interested in and committed to doing some semi-rigorous math in the adaptive dynamics framework, then this book would probably be a pretty good investment. However, if you're a biologist of any kind (including theoretical biologists) there are better places to learn about adaptive dynamics. I recommend the following as places to start:

(this one for the basic, general nuts and bolts of the theory)
Diekmann O. 2004. A beginner's guide to adaptive dynamics. Banach Center Publications n. 63, 47-86, Banach Intl. Mathematical Cntr., Warsaw, Poland.
(these for additional mathematical detail and evolutionary implications)
Dieckmann U, Marrow U, Law R. 1995. J. Theor. Biol. 176, 91-102.
Dieckmann U, Law R. 1996. J. Math. Biol. 34, 579-612.
(and for even more biological applications and implications...)
Dieckmann U, et al. 2000. "The Geometry of Ecological Interactions." Cambridge.
Dieckmann U, et al. 2004. "Adaptive Speciation." Cambridge.
Ferriere R, et al. 2004. "Evolutionary Conservation Biology." Cambridge.

Most of the chapters comprising this book are watered down versions of papers these authors and others have already published in journals. And frankly, some of those papers are not exactly seminal works in the field. One example is chapter 4, which presents an application of the theory to economics that appeared in the journal "Technovation" (yeah I know, who the heck has ever heard of that?!). An economist friend of mine thought the chapter was laughable in terms of its relevance to anything in the economic world whatsoever.

Save your money and go make copies of the relevant literature at your local university's library.