I Ergodicity and Mixing. Examples of Dynamic Systems.- 1 Basic Definitions of Ergodic Theory.- 2 Smooth Dynamical Systems on Smooth Manifolds.- 3 Smooth Dynamical Systems on the Torus.- 4 Dynamical Systems of Algebraic Origin.- 5 Interval Exchange Transformations.- 6 Billiards.- 7 Dynamical Systems in Number Theory.- 8 Dynamical Systems in Probability Theory.- 9 Examples of Infinite Dimensional Dynamical Systems.- II Basic Constructions of Ergodic Theory.- 10 Simplest General Constructions and Elements of Entropy Theory of Dynamical Systems.- 11 Special Representations of Flows.- III Spectral Theory of Dynamical Systems.- 12 Dynamical Systems with Pure Point Spectrum.- 13 Examples of Spectral Analysis of Dynamical Systems.- 14 Spectral Analysis of Gauss Dynamical Systems.- IV Approximation Theory of Dynamical Systems by Periodic Dynamical Systems and Some of its Applications.- 15 Approximations of Dynamical Systems.- 16 Special Representations and Approximations of Smooth Dynamical Systems on the Two-dimensional Torus.- Appendix 1.- Lebesgue Spaces and Measurable Partitions.- Appendix 2.- Relevant Facts from the Spectral Theory of Unitary Operators.- Appendix 3.- Proof of the Birkhoff-Khinchin Theorem.- Appendix 4.- Kronecker Sets.- Bibliographical Notes.