QUANTUM STOCHASTIC PROCESSES This course is for 4-5th year and graduate students. It is delivered in Department of Physics and ILC MSU since 1973. It is dedicated to systematic account of Quantum Stochastic Processes right in the form they are actually used in theoretical calculations of Quantum Open Systems. These methods turned to be the most useful in application to the problems of laser physics that is the reason why the most part of the specific examples are related to this field of applications of Quantum Theory. A specific feature of this course is that it is based on the most general concepts of mathematical theory of Stochastic Processes, being the same time adapted to the demands of students - physicists. This makes possible to get a systematic and very compact approach to the practically used technique. Some parts of course are based on original theoretical results obtained by the author, these parts being strictly fit to the general purpose of the course. This course is distinguished among other approaches to the problems of Quantum Open Systems by its basic concept which proved to be an appropriate one to unify all the specific physical problems into a general theory and classify them as its specific applications. The course consists of 12 up to 13 lectures, each is scheduled for two 45 minute classes. REFERENCES 1. B. A. Grishanin, Quantum Electrodynamics for Radiophysicists, Moscow State University, Moscow, 1981. 2. L. Allen, J. Eberly, Optical Resonance and Two-Level Atoms, Dover, 1987. 3. J. A. Reissland, The Physics of Phonons, Whiley&Sons, London-New York-Sydney-Toronto, 1973. The Lectures Program LECTURE 1. Quantum probability theory as an essential element of quantum mechanics. Logic of quantum events. Calculation of probabilities and average values. Quantum probabilistic space. The most important representations of quantum systems. Hierarchy of quantum mathematical objects: state space, algebra of observables and algebra of superoperators. LECTURE 2. Algebra of superoperators and its representations. Symbolic representation of syperoperator transformations with use of substitution symbol. Algebraic rules of using symbolic representations of superoperator expressions, chronological ordering. Matrix representations. Application of Dirac notations to superoperator expressions. LECTURE 3. The most important superoperators of quantum systems. Superoperator representation of two-level system dynamics. Wigner and Glauber representations. Quasiclassical asymptotics. LECTURE 4. Open systems and quantum stochastic processes. Mathematical definition of an open system and quantum stochastic process. Markovian transition superoperator and calculation of single-instant average values within Heisenberg, Scrodinger and interaction representations. Necessary and sufficient conditions of physical realizability of a transition superoperator.