this book presents a very deep and solid review of the theory of finite elements for parabolic problems. is the ideal book to dictate a graduate course on the field, as well as for learning from it as an specialist. it has a very extensive and up-to-date references list.
the reading of this book needs the knowledge of some basic theory on finite elements approximation, and a little bit of PDE's theory. However, this knowledge is not indispensable.
summarizing, it is an exelent book. rigorous but also very pedagogical, and not very difficult to read.