"The appearance in the Academic Press imprint of the twelfth edition of this book first published in 1972 gives an opportunity for a very belated notice in these pages. The first third of the book covers the elementary theory of probability, random variables, conditional probability and Markov chains. Chapter 5 focusses on the exponential distribution and Poisson processes, and then there are chapters on continuous-time Markov chains, renewal theory, queueing theory, reliability theory, Brownian motion and stationary processes, and simulation. This twelfth edition adds a short chapter on coupling and stochastic order. The treatment throughout is straightforward and fairly informal, consisting almost entirely of theory followed by examples, the latter being drawn from many different fields. Convergence theorems and the like are ignored. Nor is there any mention, for example, of sigma algebras; on page 3 we are simply given, for mutually exclusive events. Nor, at the other extreme, is there any discussion of the modelling assumptions or consideration of whether any given model is valid.

At the end of each chapter is a lengthy exercise, usually of well over thirty questions and sometimes over eighty; a small number (starred) have solutions in the back, while there is a separate free instructors' manual giving all solutions. The approach is very much that of Feller [1], while combining discrete and continuous distributions into one volume. In a book of this length and scope the index is of crucial importance; here it is mainly (but not entirely) concerned with the mathematics rather than the applications. I'm not sure how helpful this would be for users looking for information on specific applications used in the examples. That the book has continued to be reissued in new editions over a period of 47 years speaks for itself. It is obviously a most useful and wide-ranging reference resource, and it could also be used as the basis for numerous different university courses (including actuarial science), although its length, cost and bulk (over 1.5 kg) are somewhat intimidating. Apart from a few unfortunate page-breaks, the layout and other production values are excellent.

" --The Mathematical Gazette.