When the number of degrees of freedom of a wave system is very large, a deterministic description is not feasible anymore and a statistical one is required. Wave turbulence (WT) can be generally defined as the out-of-equilibrium statistical mechanics of random dispersive nonlinear waves. It has been applied to a variety of fields from quantum to astrophysical scales. WT finds its application in the description of ocean waves: the nonlinear interactions provided by the WT theory are an important ingredient in the operational ocean wave forecasting models. WT concepts have also been applied to internal waves that are responsible for the turbulent mixing in the ocean; quantized vortex lines which are important for understanding superfluids turbulence; Alfvén waves in astrophysical application; planetary Rossby waves, relevant in weather and climate studies; waves in Bose–Einstein condensates and in nonlinear optics; a great variety of waves in plasmas of fusion devices; waves on vibrating elastic plates, capillary waves, and many other physical systems. After introducing the general concepts of turbulence in fluids, the purpose of the course is to give a general and compact introduction to WT and make it accessible for graduate students and non-specialist researchers who are willing to master it and possibly to apply it in their own field of research. The course will be as self-consistent as possible, trying to insist on conceptual issues, but giving all the mathematical details needed to tackle properly the problem. The aim will be to propose a formal but yet simplified picture of the key aspects and properties of the Wave Turbulence theory and to provide insights into physical situations and practical problems. Specifically, the course will propose a general presentation of the mathematical background suitable for physicists and engineers. The different lecturers will propose examples extracted from their research fields with particular attention to surface gravity waves, elastic waves, optical waves and quantum turbulence. Differences between fluid turbulence (Navier-Stokes) and WT will be examined. The limits and failure of the Wave Turbulence theory, including the observation of the phenomenon of intermittency observed in many incoherent wave systems, will be reviewed. Finally, some interesting and new perspectives to be pursued in the future will be presented. With respect to this scope, an illustration of the more general framework of extreme events (like rogue waves in the ocean) and large deviations will be given. The course is addressed to master students, doctoral students, young and senior researchers interested in general physics, fluid mechanics, geophysics, nonlinear optics, turbulence, statistical mechanics and condensed-matter.