From the preface to the second edition: The major difference of substance between the first [Oxford: Clarendon Press (1986; Zbl 0606.60002)] and second editions of this text is the new Chapter 12 on Markov chains. This chapter is a self-contained account of discrete-time chains, culminating in a proper account of the convergence theorem. Numerous lesser changes and additions have been made to the text in response to the evolution of course syllabuses and of our perceptions of the needs of readers. These include more explicit accounts of geometrical probability, indicator functions, the Markov and Jensen inequalities, the multivariate normal distribution, and Cramér’s large deviation theorem, together with further exercises and problems often taken from recent examination papers at our home universities.