This work is a needed reference for widely used techniques and methods of computer simulation in physics and other disciplines, such as materials science. Molecular dynamics computes a molecule’s reactions and dynamics based on physical models; Monte Carlo uses random numbers to image a system’s behaviour when there are different possible outcomes with related probabilities. The work conveys both the theoretical foundations as well as applications and tricks of the trade , that often are scattered across various papers. Thus it will meet a need and fill a gap for every scientist who needs computer simulations for his/her task at hand. In addition to being a reference, case studies and exercises for use as course reading are included.