The material presented at this seminar represents the cornerstone of modern Fluid Mechanics. The first part of the seminar addresses issues in Hydrodynamics stability theory, including: (a) the basic principles and mechanisms of instabilities in fluids, such as Benard cells, Taylor vortices, stability of parallel flows, including maxing layers, jets and boundary layers, etc.; (b) weakly nonlinear theories of unbounded, incompressible and compressible mixing layers, including the derivation of Landau type evolution equations and the discussion of the type of bifurcation; and (c) fully nonlinear problems, Lorenz equations, and various scenarios leading to turbulence. The second part of the seminar is dedicated to the modern treatment of turbulence and includes: (a) the physical foundations of turbulence; (b) mathematical theories (random fields, correlations, spectral theory, Reynolds statistics); (c) statistical theory of homogeneous turbulent fields; (d) the structure of turbulent shear flows and their modeling; and (e) experimental methods and the calculation of different turbulent flows.

GALLERY