  The present note contains the text of lectures discussing the problem of
universality in fully developed turbulence. After a brief description of
Kolmogorov's 1941 scaling theory of turbulence and a comparison between the
statistical approach to turbulence and field theory, we discuss a simple model
of turbulent advection which is exactly soluble but whose exact solution is
still difficult to analyze. The model exhibits a restricted universality. Its
correlation functions contain terms with universal but anomalous scaling but
with non-universal amplitudes typically diverging with the growing size of the
system. Strict universality applies only after such terms have been removed
leaving renormalized correlators with normal scaling. We expect that the
necessity of such an infrared renormalization is a characteristic feature of
universality in turbulence.
