In this third edition, we have expanded and updated the second edition and includedmore recent developments within stochastic control and its applications.Specifically, we have replaced Section1.5on application tofinance by a morecomprehensive presentation offinancial markets modeled by jump diffusions (thenew Chap.2). We have added a new chapter on backward stochastic differentialequations, convex risk measures, and recursive utilities (Chap.4). Moreover, wehave expanded the optimal stopping chapter (was Chap. 2, now Chap.3) and thestochastic control chapter (was Chap. 3, now Chap.5) and added a new chapter onstochastic differential games (Chap.6). In addition, we have corrected errors andupdated and improved the presentation throughout the book.