The result of 15 years of teaching a final year undergraduate course on computational physics, this book summarizes developments of the stochastic phenomena in the context of physics. The approach adopted is that there is to be no canon followed in the field. Instead, the topics are chosen so as to give a feeling for the breadth of applications of Monte Carlo methods in physics. It is designed to be a reference for students wishing to gain more technical interest in the subject as a way of getting quantitative answers to a problem. The level of knowledge assumed corresponds to that of final year undergraduates, but postgraduate students in a number of disciplines should also find the material of value. It contains a number of references to research literature.