This book presents the second part of a two-volume series devoted to a sys- tematic exposition of some recent developments in the theory of discrete- time Markov control processes (MCPs). As in the first part, hereafter re- ferred to as "Volume I" (see Hernandez-Lerma and Lasserre 1]), interest is mainly confined to MCPs with Borel state and control spaces, and possibly unbounded costs. However, an important feature of the present volume is that it is essentially self-contained and can be read independently of Volume I. The reason for this independence is that even though both volumes deal...