The essential point in computational physics is not the use of machines, but the systematic application of numerical techniques in place of, and in addition to, analytical methods, in order to render accessible to computation as large a part of physical reality as possible. The various available techniques, disparate as they may seem, are traced back to only three main methodological sources; finite difference calculus, linear algebra, and stochastics. Each algorithm is carefully introduced and every computational tool is explained in terms of fundamental numerical techniques. Examples from statistical mechanics, quantum mechanics, and hydrodynamics are employed to bridge the gap between basic methodology and modern research. This second edition of Franz Vesely's renowned textbook takes into account the new vistas that have opened up recently in this rapidly evolving field. Furthermore, web-based sample programs augment the text.