From the preface to the first edition. Asymptotic distribution theorems in probability and statistics have from the beginning depended on the classical theory of weak convergence of distribution functions in Euclidean spat-onvergence, that is, at continuity points of the limit function. The past several decades have seen the creation and extensive application of a more inclusive theory of weak convergence of probability measures on metric spaces. There are many asymptotic results that can be formulated within the classical theory but require for their proofs this more general theory, which thus does not merely study itself. This book is about weak-convergence methods in metric spaces, with applications sufficient to show their power and utility.