The aim of this talk is to present the construction of equilibrium states for the billiard map, using appropriate transfer operators acting on anisotropic Banach spaces. We first present the general motivations in Dynamical Systems -- statistics of an orbit, invariant measures, etc. -- with many toy examples. Then we introduce the notions of entropy, pressure, the variational principle and equilibrium states. From all this, we present the dynamics of a Sinai Billiard, as well as recent results. Finally, we introduce the construction of the appropriate anisotropic Banach spaces and their use through a transfer operator to construct equilibrium states. If time permits, we present a work in progress concerning the measure of maximal entropy for the Billiard Flow and its relation to a specific equilibrium state for the billiard map.