EN
The purpose of the paper is to present in a concise manner the key theoretical issues related to mathematical modelling in political science, alongside selected examples of using mathematical modelling in research practice. In the process, the function of scientific models in the development of scientific theories is discussed, indicating the main types of scientific models. Then, selected elements of the theory of mathematical models are considered and the most common misunderstandings in using the language of mathematics in political science studies are described. Finally, selected examples of using mathematical models in studies of political phenomena are presented: a quadratic-hyperbolic model of the real global GDP growth dynamics and a game theory model of the transmission of cooperative behaviours among political elites were developed. The R programme was used to build the models.