This book is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include: indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real- world problems; attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject; and providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks. Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.