We continue with thermodynamic formalism from last time, this time applying what we have learned to hyperbolic dynamical systems. In particular, we shall see how thermodynamic formalism can be applied to obtain information about fractal dimensions of hyperbolic sets (which is, in a sense, a measure of complexity of the system). In particular, we shall cover: the Bowen's equation (relating topological pressure to Hausdorff dimension), which is a very broad generalization of Moran's theorem for some iterated function systems, as well as Ruelle's theorem (asserting that, in some sense, only observables at periodic points are needed to completely determine Bowen's equation). If time permits, we shall describe an approach, using thermodynamic formalism, to one of the open problems in spectral theory of quasiperiodic Schroedinger operators, that was presented by Anton Gorodetski at the seminar on Oct. 16th.