Kolmogorov Spectra of Turbulence I

0. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 1.1 The Hamiltonian Formalism for Waves in Continuous Media.- 1.2 The Hamiltonian Formalism in Hydrodynamics.- 1.3 Hydrodynamic-Type Systems.- 1.4 Spin Waves.- 1.5 Universal Models.- 2. Statistical Description of Weak Wave Turbulence.- 2.1 Kinetic Wave Equation.- 2.2 General Properties of Kinetic Wave Equations.- 3. Stationary Spectra of Weak Wave Turbulence.- 3.1 Kolmogorov Spectra of Weak Turbulence in Scale-Invariant Isotropic Media.- 3.2 Kolmogorov Spectra of Weak Turbulence in Nearly Scale-Invariant Media.- 3.3 Kolmogorov Spectra of Weak Turbulence in Anisotropic Media.- 3.4 Matching Kolmogorov Distributions with Pumping and Damping Regions.- 4. The Stability Problem and Kolmogorov Spectra.- 4.1 The Linearized Kinetic Equation and Neutrally Stable Modes.- 4.2 Stability Problem for Kolmogorov Spectra of Weak Turbulence.- 4.3 Nonstationary Processes and the Formation of Kolmogorov Spectra.- 5. Physical Applications.- 5.1 Weak Acoustic Turbulence.- 5.2 Wave Turbulence on Water Surfaces.- 5.3 Turbulence Spectra in Plasmas, Solids, and the Atmosphere.- 6. Conclusion.- A. Appendix.- A.1 Variational Derivatives.- A.2 Canonicity Conditions of Transformations.- A.3 Elimination of Nonresonant Terms from the Interaction Hamiltonian.- References.