The third edition of this text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and should provide a taste and encouragement for more advanced work.There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The books begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; in concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition.