This 4th edition is a major revision of Vol. II is the leading two-volume dynamic programming textbook by Bertsekas. It contains a substantial amount of new material and
a reorganization of old material. The length has increased by over 60% from the third edition, and
most of the old material has been restructured and/or revised. Volume II now has more than 700 pages and is larger than Vol. I. It can arguably be viewed as a new book!

Approximate DP has become the central focal point of Vol. II, and occupies more than half of the book (the last two chapters and large parts of Chapters 1-3). Thus, one may also view Vol. II as a followup of the author's 1996 book ``Neuro-Dynamic Programming" (coauthored with John Tsitsiklis). The present book focuses, to a great extent, on new research that became available after 1996. On the other hand, the textbook style of the book has been preserved, and some material has been explained at an intuitive or informal level while referring to the journal literature or the Neuro-Dynamic Programming book for a more mathematical treatment.