Computer simulation is increasingly used in physics and engineering to predict the probable outcome of experiments and to aid in their interpretation. The methods of simulation are based on a range of numerical techniques for treating ordinary and partial differential equations. Since much of physics can be broken down into a relatively small set of fundamental equations, a few general methods can be widely applied. This text aims to give an introduction to those methods suitable for readers at an undergraduate level and for those studying the subject for the first time at the graduate level. The methods are illustrated with simple programs and problems. The book covers a range of material not available in other introductory texts.