The main purpose of the book is to introduce some progress on probability theory and its applications to physics， made by Chinese probabilists，especially by a group at Beijing Normal University in the past 15 years. Up to now， most of the work is only available for the Chinese-speaking people.In order to make the book as self-contained as possible and suitable for a wider range of readers， a fundamental part of the subject， contributed by many mathematicians from different countries， is also included. The book starts with some new contributions to the classical subject-Markov chains，then goes to the general jump processes and symmetrizable jump processes，equilibrium particle systems and non-equilibrium particle systems. Accordingly the book is divided into four parts. An elementary overlook of the book is presented in Chapter 0. Some notes on the bibliographies and openproblems are collected in the last section of each chapter. It is hoped that the book could be useful for both experts and newcomers， not only for mathematicians but also for the researchers in related areas such as mathematicalphysics， chemistry and biology.