From the reviews:
SIAM REVIEW
The presentation of this book is systematic and self-contained...Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) course...This book is highly recommended to anyone who wishes to study the relationship between Pontryagin's maximum principle and Bellman's dynamic programming principle applied to diffusion processes.
MATHEMATICS REVIEW
This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. Review