This book shares the dictum of J. L. Doob in treating probability theory as a branch of measure theory and establishes this relationship early. Probability measures in product spaces are introduced right at the start as a way of laying the groundwork to later claim the existence of stochastic processes with prescribed finite-dimensional distributions.

Other topics analyzed in the book include supports of probability measures, zero-one laws in product measure spaces, the Erdös-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains.

This book is offered as a textbook for students pursuing graduate programs in mathematics and/or statistics. The book aims to help teachers present the theory with ease and to help students sustain their interest and joy in learning the subject.