  This is an introductory course on the open problems in the theory of fully
developed turbulence. It discusses: 1. hydrodynamical equations, 2. existence
of solutions, 3. statistical description of turbulent flows, 4. Kolmogorov
scaling theory, 5. functional approach to turbulence: similarities and
differences with field theory, 6. breakdown of the Kolmogorov theory in a
passive scalar model, 7. inverse renormalization group.
