I.1. The Criteria of the Relative Degree of Order of the States of Open Systems -- I.2. Connection Between the Statistical and the Dynamic Descriptions of Motions in Macroscopic Open Systems. The Constructive Role of Dynamic Instability of Motion -- I.3. The Transition from Reversible to Irreversible Equations. The Gibbs Ensemble in the Statistical Theory of Nonequilibrium Processes -- I.4. The Role of Fluctuations at Different Levels of Description. Fluctuation Dissipation Relations -- I.5. Brownian Motion in Open Systems. Molecular and Turbulent Sources of Fluctuations -- I.6. Laminar and Turbulent Motion -- 1. Evolution of Entropy and Entropy Production in Open Systems -- 1.1. Chaos and Order. The Controlling Parameters. Physical Chaos. Evolution and Self-Organization in Open systems -- 1.2. Boltzmann-Shannon-Gibbs Entropy -- 1.3. Entropy Distribution Function -- 1.4. The Gibbs Ensemble. Smoothing over the Physically Infinitesimal Volume. Entropy Including Fluctuations. Space (Time) and Phase Averages. Local Ergodicity Condition -- 1.5. The Kinetic Boltzmann Equation for Statistical and Smoothed Distribuions. Physically Infinitesimal Scales. The Constructive Role of the Dynamic Instability of Motion of Atoms in a Gas -- 1.6. The Role of Nonequilibrium Fluctuations in a Boltzmann Gas. Molecular and Turbulent Sources of Fluctuations -- 1.7. The Kinetic Equations for the N-Particle Distribution Functions. The Leontovich Equation -- 1.8. Boltzmann's H-Theorem for Smoothed (Pulsating) and Deterministic Distributions -- 1.9. Entropy and Entropy Production for Smoothed and Deterministic Distributions -- 1.10. The Gibbs' Theorem -- 1.11. H-Theorem for Open Systems. Kulback Entropy -- 1.12. Evolution in the Space of Controlling Parameters. The S-Theorem -- 1.13. The S-Theorem. Local Formulation -- 1.14. The Comparison of the Relative Degree of Order of States on the Basis of the S-Theorem Using Experimental Data -- 1.15. Dynamic and Statistical Descriptions of Complex Motions. K-Entropy, Lyapunov Indices. Nonlinear Characteristics of the Trajectory Divergence -- 1.16. Criteria of Dynamic Instability of Motion in Statistical Theory -- 1.17. Entropy as Measure of Diversity in Biological Evolution -- 1.18. The Principle of Minimum Entropy Production in Self-Organization Processes -- 2. Transition From the Reversible Equations of Mechanics to the Irreversible Equations of the Statistical Theory -- 2.1. Two Types of Reversible Processes. Symmetry Properties of Distribution Functions -- 2.2. Liouville Equation and Vlasov Equation. The First Moments and the "Collisionless" Approximations -- 2.3. Reversible Equations in Quantum Statistical Theory -- 2.4. Two Types of Dissipative Kinetic Equations for N-Particle Distributions -- 2.5. Measure of Deficiency (Incompleteness) of the Statistical Description -- 2.6. The Hierarchy of Equations of Fluid Mechanics -- 3. Fluctuation Dissipation Relations -- 3.1. Examples of Fluctuation Dissipation Relations -- 3.2. FDR for N-Particle Distribution Functions -- 3.3. Thermodynamic Form of the FDR. The Callen-Welton Formula -- 3.4. FDR for a Boltzmann gas. The Fluctuative Representation of Boltzmann Collision Integral -- 3.5. FDR for Large-Scale (Kinetic) Fluctuations -- 3.6. Examples of FDR for Large-Scale Fluctuations -- 3.7. System of Quantum Atoms Oscillators -- 3.8. Fluctuation Dissipation Relations in Hydrodynamics -- 3.9. Two Ways of Defining Kinetic Coefficients -- 3.10. The Molecular Langevin Source in the Difffusion Equation -- 3.11. Connection between the Intensities of Langevin Sources and the Correlator of of Phase Density Fluctuations -- 3.12. Natural Flicker Noise ("1/f Noise"). FDR for Flicker Noise -- 3.13. Natural Flicker Noise and Superconductivity -- 4. Brownian Motion -- 4.1. Fokker-Planck and Langevin Equations -- 4.2. Three Definitions of the Langevin and Fokker-Planck Equations -- 4.3. The Fokker-Planck Equations in the Statistical Theory of Nonequilibrium Processes -- 4.4. Transition to the Fokker-Planck Equation from the Smoluchowski equation (the Chapman-Kolmogorov Equation) and from the Master Equation -- 4.5. Langevin.Sources in Kinetic Equations -- 4.6. Langevin Sources in Fokker-Planck and Einstein-Smoluchowski Equations -- 4.7. Turbulent Langevin Sources and Fluctuation Dissipation Relations in Hydrodynamics -- 4.8. Brownian Motion in Systems with a Variable Number of Particles. -- 5. The Boltzmann-Gibbs-Shannon Entropy As Measure of the Relative Degree of Order in Open Systems -- 5.1. Van der Pol Generator -- 5.2. Generator with Inertial Nonlinearity -- 5.3. Invariant Measures. Examples of Gibbs Distributions for Open Systems -- 5.4. Generalized Van Der Pol Generators. Bifurcations of the Limiting Cycle Energy and the Period of Oscillations -- 5.5. Dynamic and Statistical Distributions -- 5.6. Comparison Between the Degrees of Order in the Bifurcation Points and in the State of Dynamic Chaos -- 5.7. Evolution of Entropy in Systems with Two Controlling Parameters -- 5.8. A Medium of Linked Generators. The Kinetic Approach in the Theory of Self-Organization -- 5.9. A System of Van der Pol Generators with Common Feedback. Associative Memory and Pattern Recognition -- 5.10. Kinetic Description of Chemically Reacting Systems -- 5.11. A Medium of Bistable Elements. The Kinetic Approach in the Theory of Phase Transitions -- 6. Turbulent Motion. The Structure of Chaos -- 6.1. Characteristic Features of Turbulent Motion. The Main Problems -- 6.2. Incompressible Fluid. Reynolds Equations. Reynolds Stresses -- 6.3. Well-Developed Turbulence. Turbulent Viscosity -- 6.4. Semiempirical Prandtl-Karman Theory of Turbulence -- 6.5. Onset of Turbulence in Steady Couette and Poiseuille Flows -- 6.6. Entropy Production in Laminar and Turbulent Flows -- 6.7. The Principle of Least Dissipation and the Principle of Minimum Entropy Production in Self-Organization Processes -- 6.8. Evolution of Entropy in the Transition from Laminar to Turbulent Flow -- 6.9. Kinetic Description of Hydrodynamic Motion -- Conclusion -- References.