The aim of this thesis was to get acquainted with point processes and their moment measures. In the first chapter, we introduce the basic concepts needed to understand the rest of the work. After the definition of point measure, a precise definition of point process is given. We have presented the mathematical tools which are used for characterization of the point processes distribution. The most important examples of point processes that illustrate the main concepts are given. In addition, we introduce with stationary point processes. There is the definition of contact distance of the process from the given point and its distribution is brought into connection with the capacity functional. We continue with the definition of the intensity measure as the expectation of a random variable that represents the number of points in a given area. Campbell’s formula is used to calculate expected value of random variable \(\sum_{x \in X}f(x)\), which is proved by Lebesgue induction. Second moment measures and second moment density are defined as well. We present the second moment measures of stationary point processes and the \(K\)-function that describes the interaction between points. We illustrate the application of \(K\)-function on real data. Finally, we define Janossy measures that we connect with the distribution of point processes and their moment measures.