This second edition differs profoundly from the first—and not only in having two authors rather than one. We retain the Gallic tradition of dividing the volume into three massive chapters: Chapter I, which says why the subject is worth studying; Chapter II, which provides background; and Chapter III, which presents an account of Markov processes. Chapter I is now much more extensive and wide-ranging, and covers much work done since the first edition appeared. Chapter II is now a highly systematic account, with detailed proofs, of what every young probabilist must know. It is rather unashamedly a sequel to DW's Probability with Martingales, Cambridge University Press having been very generous in allowing us to follow that account closely (but without many proofs, without the examples, etc.). It is perfectly possible to read Chapter II before Chapter I if you so wish. We would suggest however that you try things in the order ‘heuristics then rigour’:

Chapter III seems to have been regarded as the most successful part of the original; and it is reproduced here without much modification (except that some of the functional analysis is given fuller treatment). It was always intended as a missionary tract on Markov processes. The full theory may be found in Sharpe [1] and in the final two volumes of the probabilist's bible, Dellacherie and Meyer [1].