From the reviews:“The first volume is devoted to ergodic theory and dynamical systems. It contains 19 papers divided into four groups … . The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinai’s personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results.” (Nikolai Chernov, Mathematical Reviews, Issue 2012 e)

• Entropy Theory of Dynamical systems.- On the Notion of Entropy of a Dynamical System.- Construction and Properties of Invariant Measurable Partitions.- Weak Isomorphism of Transformations with Invariant Measure.- Dynamical Systems with Countably-Multiple Lebesgue Spectrum. I.- Dynamical Systems with Countably-Multiple Lebesgue Spectrum. II.- Ergodic theory and Number Theory.- Renewal-type limit theorem for the Gauss map and continued fractions.- A Limit Theorem for Birkhoff Sums of non-Integrable Functions over Rotations.- Mixing for Some Classes of Special Flows Over Rotations of the Circle.- Smoothness of conjugacies of diffeomorphisms of the circle with rotations.- Feigenbaum universality and the thermodynamic formalism.- The Theory of hyperbolic dynamical systems Markov Partitions and thermodynamic Formalism.- Markov Partitions and C-Diffeomorphisms.- Gibbs Measures in Ergodic Theory.- Gibbs measures for partially hyperbolic attractors.- Steady-State Electrical Conduction in the Periodic Lorentz Gas.- Space-time chaos in the system of weakly interacting hyperbolic systems.- Billiards.- Dynamical Systems with Elastic Reflections.- On a Fundamental Theorem in the Theory of Dispersing Billiards.- Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls.- Billiard Trajectories in a Polyhedral Angle.