Solving problems in multiple areas of science often requires calculating the values of integrals. However, the process of integration is so complex that sometimes it is not possible to determine the exact value of an integral. There are various numerical integration methods that offer efficient algorithms for calculating the approximate solution. Still, in certain cases (e.g. multidimensional problems), due to insufficient speed or impracticality of the performance they can get significantly complicated. In this thesis, we described a different method of integration - the Monte Carlo method. This method allows us to get appropriate estimated values of integrals and their approximation error. This approximate method is also used in situations when the problem is too difficult (or impossible) to solve analytically. It is especially useful when solving multidimensional problems because the accuracy of the estimated value does not depend on the dimension of space. Hence, using this method is both common and desirable in modern times. Primary goal of this thesis was to describe Monte Carlo integration method and to elaborate on it theoretically. It was concluded that the whole process of using this method is based on the idea of efficiently generating random variables from a certain distribution. In addition, we named some of the methods used for generating such variables. It is worth pointing out that it is necessary to carefully select the Monte Carlo estimator i.e. the distribution from which we generate random variables. Namely, it is on that selection of the distribution that the variance of the estimator which we are trying to maximally reduce depends on. This process of reduction of the variance of the Monte Carlo estimator was described using the Importance Sampling method which has proven to give a better estimated value of the integral than the “naive” Monte Carlo method.