Introduction -- Wave Trubulence as a Part of General Turbulence Theory -- For the Impatint: a WT Cheatsheet -- Solutions to Exercises -- Statistical Objects in Wave Turbulence -- Wave Turbulence Formalism -- Solutions to Exercises -- Conserved Quantities in Wave Turbulence and Their Cascades -- Steady State and Evolving Solutions for the Wave Sepctrum -- Finite-Size Effects in Wave Turbulence -- Properties of the Higher-order Statistics. Intermitency and WT Life Cycle -- Solutions to Exercises -- Nonlocal Drift/Rossby Wave Turbulence -- Magneto-Hydrodynamic Trubulence -- Bose-Einstein Condensation -- List of Projects.

Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.