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Abstract: The Monte Carlo method is a wide spread numerical method which is used in a lot of different areas of numerical calculations.This thesis gives a short introduction to the method.In the introduction we give a short resume and history of the method.One area of major interest in the use of Monte Carlo methods is the generation of random numbers and sampling from given distribution functions; this is discussed in the next chapters.Then follows a description of the method and various aspects of the performance are discussed.Variance reduction plays a big role in the Monte Carlo theory and the most common topics are covered.To illustrate the use of Monte Carlo methods we give some examples of applications from the domain of particle transport.A revision of probability theory and an mathematical justification of the method is included in the appendices.