This text has three main aims: to provide an introduction to probability without exposing the reader to overmuch measure theory, to discuss a wide range of random processes in some depth with many examples, and to give the beginner some flavour of more advanced work, by suitable choice of material. The book begins with basic material commonly covered in first-year undergraduate mathematics and statistics courses, and finishes with topics to be found in graduate courses. Features of this new edition include: new and expanded sections in the early chapters providing more illustrative examples and introducing more ideas early on; two new chapters providing more comprehensive treatment of the simpler properties of martingales and diffusion processes; and more exercises at the ends of almost all sections, with many new problems at the ends of chapters. The companion volume "Probability and Random Processes: Problems and Solutions" includes complete worked solutions to all exercises and problems of this edition. The book should be useful as a text for mathematics and natural science undergraduates at all levels from first to final-year degree work and useful as a reference book for graduates and all those interested in the applications of probability theory.

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