This paper presents the theoretical foundations of the Koopman operator. It is a linear operator that transforms nonlinear dynamical systems into linear systems. The trade-off of this transformation is the abandonment of the finiteness of the dimensions of the system in favor of an infinite number of dimensions. Only the rapid development of computers made it possible to solve such problems. One of the most commonly used algorithms for this problem is the DMD (Dynamic Mode Decomposition) algorithm. It is a data-driven algorithm, i.e., for the system analysis, it is not necessary to know the equations describing the system, but the whole analysis is based on the inclusion of measured data at different points in time. For testing purposes, data from several examples of fluid dynamics were processed using OpenFOAM simulations. It was found that it is possible to reconstruct the picture of the observed variables for a small number of modes and that a given system can be described with several eigenmodes and eigenvalues. In addition to the analyzes of the flows, an analysis of the data obtained during the Sars-Cov 2 virus epidemic was also performed. Prediction of the evolution of the epidemic is possible with carefully chosen analysis settings such as the size of the training data. The accuracy of the prediction itself depends on the number of days observed. At the end of the paper, the main considerations and suggestions for future implementations of this method are given.