The game theory relates to the study of multipersonal decision problems, those that imply the explicit agreement between the agents or players (cooperative games), as well as those that are solved through individual decisions without the possibility to establish binding agreements among the agents (non-cooperative games). The goal of the course is to set forth the elementary notions of the game theory, as well as the economic applications that derive from it and that motivate it at the same time. The central concept will be the analysis of the derivative profits of forming coalitions. In particular, we will focus on the cooperative games of transferable utility, the goal of which is, to study the formation of these coalitions and to analyze the criteria of distribution of the profits.