This set of lectures is the outgrowth of a new course in the Department of Materials Science at Stanford University. It was taught collectively by the authors of the various sections and represents an attempt to increase the awareness of students in the materials area of computer simulation techniques and potentialities. The topics often ranged far afield from the materials area; however, the total package served the intended purpose of being an initiation into the world of computer simulation and, as such, made a useful first iteration to the intended purpose. The second iteration, which is in process, deals exclusively with the materials area. The course was designed to teach students a new way to wrestle with "systems" problems in the materials science work area that require the synthesis and interactions of several disciplines of knowledge. This course was a response to the realization that effective handling of real problems, which are essentially systems problems, is one of the most important attributes of a graduate materials scientist. About a third of the course was devoted to the student's selected problem, in the materials area, which he simulated using the digital computer.