The course presents basic notions of the mathematical game theory. Different types of games are discussed together with different possibilities how to formalize them mathematically and how to solve them algorithmically. At the beginning, the combinatorial games are discussed, i.e., games played by two players with perfect information. Then the games in the games in the standard (strategic) and in the extensive form are studied, where we start with two-person zero-sum games (that can be solved in a finite case by transformation to the linear programming problem), and then we continue with two-person general-sum games. When the general-sum games are discussed, there are distinguished two case: non-cooperative games, where existence of Nash equilibria is studied, and cooperative games, where we distinguish variants with transferable utility and with nontransferable utility. When studying both zero-sum and general-sum games, the variants of the games extended with
probabilistic moves and an incomplete information are also studied.