This book is a very good text on empirical processes. There are some previous monographs in this subject, for example, those by D. B. Pollard [Empirical processes: theory and applications, Inst. Math. Statist., Hayward, CA, 1990; MR 93e:60046], R. M. Dudley [in Ecole d'ete de probabilites de Saint-Flour, XII---1982, 1--142, Lecture Notes in Math., 1097, Springer, Berlin, 1984; MR 88e:60029], E. Gine-Masdeu and J. Zinn [in Probability and Banach spaces (Zaragoza, 1985), 50--113, Lecture Notes in Math., 1221, Springer, Berlin, 1986; MR 88i:60063] and P. Ganssler [ Empirical processes, Inst. Math. Statist., Hayward, CA, 1983; MR 86f:60044]. There are many differences between all these monographs. The book under review is a more complete and detailed exposition on empirical processes and their applications. It also covers the most recent developments in the area. There are three parts in the book. The first part is a thorough treatment of the convergence of stochastic processes in the absence of measurability: weak convergence, convergence in probability and almost sure convergence. Various topics on the handling of nonmeasurable random variables and processes are developed, such as outer integrals and measurable majorants. The definition of weak convergence used is the one due to J. Hoffmann-Jorgensen [Stochastic processes on Polish spaces, Aarhus Univ., Aarhus, 1991; MR 95a:60047]. This very general definition allows one to define weak convergence, even in common cases where measurability problems appear. This definition has become the standard one used in the empirical processes literature. The theory of weak convergence in the book by P. Billingsley [Convergence of probability measures, Wiley, New York, 1968; MR 38 #1718] is inadequate in some situations. Besides this, convenient definitions, generalizing the concepts of convergence in probability and almost sure convergence for not necessarily measurable sequences of random variables, are stated and their properties are explained. These definitions were introduced by Dudley [in Probability in Banach spaces, V (Medford, Mass., 1984), 141--178, Lecture Notes in Math., 1153, Springer, Berlin, 1985; MR 87e:60045]. The authors not only present an exposition of the Hoffmann-Jorgensen and Dudley theory in a coherent and understandable way, but they also complement it by giving some new results. The second part of the book is devoted to the law of large numbers and the central limit theorem for empirical processes indexed by a general class of functions. The main conditions discussed are VC classes of sets and functions (classes of functions satisfying a uniform integral condition in the entropy) and classes of functions satisfying a bracketing entropy condition. Other topics considered are the central limit theorem for functions that are either smooth, monotone, convex or Lipschitz, limit theorems holding uniformly over a class of underlying distributions, permanence of the limit theorems, and partial-sum processes and inequalities for the tails of an empirical process. The third part of the book deals with applications of empirical processes to statistics. The main topics covered are limit theorems for $M$-estimators, the delta method, rates of convergence of some estimators, the bootstrap, the convolution theorem and the minimax theorem. Some results, applying empirical processes, to obtain asymptotic normality (or even convergence to a nonnormal limit with an unusual rate) of $M$-estimators are developed. The most interesting fact in the section on rates of convergence is that the rates of convergence are related with entropy numbers. In the section on the bootstrap, not only is the i.i.d. bootstrap considered, but also the general bootstrap with respect to exchangeable weights. The book is very carefully written. It is almost free of typos. The exposition is quite clear. The material was choosen sensibly. From the preface: "Much of the theory presented in Part 2 has previously been scattered in the journal literature and has, as a result, been accessible only to a relatively small number of specialists. In view of the importance of this theory for statistics, we hope that the presentation given here will make this theory more accessible to statisticians as well as to probabilists interested in statistical applications." This is accomplished up to a point. The material that is presented is presented very clearly and the treatment is quite accessible. However, it could be difficult for a reader to look for further references on some topics. Every chapter ends with a section with bibliographical comments, although the original source of the material presented is not always mentioned. Sometimes, key results in the theory are not mentioned. For example, the characterization of the law of large numbers for empirical processes given by M. Talagrand [Ann. Probab. 15 (1987), no. 3, 837--870; MR 88h:60012] is not mentioned. The characterization of the central limit theorem for the empirical processes of characteristic functions given by M. B. Marcus [Ann. Probab. 9 (1981), no. 2, 194--201; MR 82g:60048] is also not mentioned. Reviewed by Miguel A. Arcones