This is an introduction to the modern theory of probability and stochastic processes. The aim is to enable the student to have access to the many excellent research monographs in the literature. It might be regarded as an updated version of the textbooks by Breiman, Chung, and Neveu, just to name three.
　　The book is based on the lecture notes for a two-semester course which I have offered for many years. The course is fairly popular and attracts grad uate students in engineering, economics, physics, and mathematics, and a few overachieving undergraduates. Most of the students had familiarity with elementary probability, but it was safer to introduce each concept carefully and in a uniform style,
　　As Martin Barlow put it once, mathematics attracts us because the need to memorize is minimal. So, only the more fundamental facts are labeled as theorems; they are worth memorizing. Most other results are put as propo- sitions, comments, or exercises Also put as exercises are results that can be understood only by doing the tedious work necessary. I believe in the Chinese proverb: I hear, I forget; I see, I remember; I do, I know.
　　I have been considerate: I do not assume that the reader will go through the book line by line from the beginning to the end. Some things are re called or re-introduced when they are needed. In each chapter or section, the essential material is put first, technical material is put toward the end. Sub-hea-dings are used to introduce the subjects and results; the reader should
　　have a quick overview by flipping the pages and reading the headings.
　　The style and coverage is geared toward.the theory of stochastic processes, but with some attention to the applications. The reader will find many in- stances where the gist of the problem is introduced in practical, everyday language, and then is made precise in mathematical form. Conversely, many a theoretical point is re-stated in heuristic terms in order to develop the intuition and to provide some experience in stochastic modeling.