This book claims that it aims itself towards a general audience, rather than towards an academic audience. They also claim that they aren't offering advice so much as an explanation for why fathers parent the way that they do. Generally speaking, I find that those two claims are hard to reconcile. In my experience, non-academic fathers generally want a book that offers them practical advice, while academics want lots of cutting-edge science written in scientific lingo. So in that regard, it's hard to evaluate this book.
As an academic exercise, it's pretty good. Gray and Anderson are both professors who study fatherhood from a biological/evolutionary perspective. The book covers a wide range of topics, from hormones, to paternity, to cross-cultural models of parenting. In general, I found that it was a pretty good introduction to the topic. I found that the book was at its best when focusing on each author's specialty (paternity-Anderson, hormones-Gray). Experts in the field will probably find a few bits of information in here that they didn't know before, as it's relatively comprehensive and current. That said, I found that there were some minor errors or discrepancies in the authors' data.
The writing in the book is not aimed at too high of an audience, but again, it's perhaps not practical enough to be of great use for the average reader. As a father, it was hard to take home specific suggestions based on the text without already knowing the theory. I would have liked to have seen the chapter on the effects of fathers on their children expanded, as this is really what matters most for fathers, researchers, and society in general. The mechanisms of fatherhood are important, but really, it's what fathers do for their children that matters most to most people. Overall then, I found that this was an interesting book. I think it struggles a little in trying to be both an academically rigorous book as well as a general book for fathers, and doesn't quite reach either goal. Still, it's worth a read if the topic is of interest to you. I'd still recommend Sarah Hrdy's Mother Nature as the best book of parenting, but as she generally neglects fathers in the book, Fatherhood: Evolution and Human Paternal Behavior can help fill in some of those gaps.