Navier-Stokes equations. Vorticity dynamics. Statistical description of turbulent flows. Coherent structures. Isotropic turbulence (spectral formalism, Kolmogorov theory). Anisotropic turbulence (SO(3) formalism). Discussion on the existence and uniqueness of solutions of the Navier-Stokes equations. Eddy viscosities. Point vortices. Passive scalars. Direct numerical simulation.