Ever since Yu. V. Prohorov wrote his fundamental paper "Convergence of random processes and limit theorems in the theory of probability" in the year 1956 [33], the general theory of stochastic processes has come to be regarded as the theory of probability measures in complete separable metric spaces. The subsequent work of A. V. Skorohod of which a detailed account is given in the book by I. I. Gikhman and A. V. Skorohod [9] gave a great impetus to the subject of limit theorems in probability theory. The present monograph deals with the general theory of probability measures in abstract metric spaces, complete separable metric groups, locally compact abelian groups, Hilbert spaces, and the spaces of continuous functions and functions with discontinuities of the first kind only. Emphasis is given to the work done by the Indian School of probabilists consisting of, among others, V. S. Varadarajan, R. Ranga Rao, S. R. S. Varadhan, and the author.