As a PhD student, how do I benefit from reviewing a book my adviser is writing? My adviser is writing a book for a course in computer science he will be teaching next fall and I will be the teaching assistant for that course. He wants me to review the book and go through the problems and give him feedback on both. 

He didn't say that I will get rewarded or recognized for my work in reviewing the book or the exercises associated with it, but I am guessing that my name will be mentioned in the thank you notes section at the beginning of the book, as usual with most published books based on courses. So my questions are as follows


What benefits do I get from doing this review, if any?
Also, is this work considered part of being a teaching assistant?
You'll gain his trust, if you do a good job. You will also gain a deeper understanding of the material as you'll read it thoroughly not just to learn it, but also having to think about how the material is presented. Don't expect anything else.