In this paper we are studying games with incomplete information, also known as Bayesian games. We have divided Bayesian games into two types, static and dynamic, where each of the types are studied in separate chapters. There is one more chapter dedicated to an application of Bayesian games in real life, auctions. Static Bayesian games consist of simultaneous moves made by players, after which the game ends. This chapter we open with a motivational example that shows us necessary definitions to transform a game we start with into one we can solve. In the same chapter, we give definitions and rules about Bayesian games that we later on, for dynamic Bayesian games, generalize. These definitions and rules refer to introducing types of players, which transforms a game with incomplete information (about the utility function) into a game with imperfect information (about the types of players). By defining Bayesian equilibrium we notice the equivalence between equilibria calculated before and after "the signal", the moment when the players find out their type. We also show that Bayesian equilibrium is actually Nash equilibrium of the equivalent, transformed game. We finish the chapter about static Bayesian games with a modified example of Battle of the Sexes, where the number of types of players is continuous. In dynamic games player's moves aren't necessarily simultaneous. Chapter Dynamic Bayesian games we begin by introducing a special case of dynamic Bayesian games, "signaling" games. Here as well we start with a motivational example and a graphical representation of the game, also called an extensive form. We then study dynamic Bayesian games in general, where in addition to generalized definitions introduced in the chapter about static Bayesian games, we define a modification of a subgame in a game with complete information. Further more, using that modification we define PBE (perfect Bayesian equilibrium), a special kind of Bayesian equilibrium and we finish the chapter with an interesting example of a perjury trap where we apply newly defined terms. The last chapter deals with auctions, a very successful application of Bayesian games. We consider different types of auctions (which are still used nowadays) and their equilibria. We finish the chapter with an example of an auction where we in addition to finding equilibria regarding players, we also consider the position the seller is in and which of the two auctions considered in the example are more profitable for him.