This book is a text at the introductory graduate level, for use in the one semester or two-quarter probability course for first-year graduate students that seems ubiquitous in departments of statistics, biostatistics, mathemat ical sciences, applied mathematics and mathematics. While it is accessi ble to advanced ("mathematically mature") undergraduates, it could also serve, with supplementation, for a course on measure-theoretic probability. Students who master this text should be able to read the "hard" books on probability with relative ease, and to proceed to further study in statistics...