For those who know the already classic work of Billingsley, "Convergence of Probability Measures", this big and important volume will immediately appear as an update -- together with various generalizations -- of the theory of convergence in distribution and of empirical stochastic processes already presented by Billingsley. The work is divided into three parts, each of which contains different chapters; the title of the three parts are: Stochastic Convergence, Empirical Processes, Statistical Applications. Many of the theorems that are in the various chapters, some of which difficult to find up until now, are for the first time put together in a single volume. Of particular interest for statisticians is the third part, of which we point out among other things, the important convergence theorems concerning the asymptotic behavior of sample statistics and the convergence rates in semiparametric estimation, and the applications to bootstrap and to the functional delta method. There is no need to warn that the reading of this work is very involved and requires a deep knowledge of modern probability calculus.