A description of the many facets of the Monte Carlo Method is presented. The subject is traversed from the most elementary to the more difficult techniques, and from the least practical to the most fruitful applications. The generation of random numbers in the modern electronic computing machine is dealt with. Most of the material is of an expository nature, but the section on the solution of elliptic partial differential equations with certain boundary conditions is new. Some general remarks on evaluating the method are given. (W.D.M.)