  The lectures presented by one of us (IP) at the Les Houches summer school
dealt with the scaling properties of high Reynolds number turbulence in fluid
flows. The results presented are available in the literature and there is no
real need to reproduce them here. Quite on the contrary, some of the basic
tools of the field and theoretical techniques are not available in a
pedagogical format, and it seems worthwhile to present them here for the
benefit of the interested student. We begin with a detailed exposition of the
naive perturbation theory for the ensemble averages of hydrodynamic observables
(the mean velocity, the response functions and the correlation functions). The
effective expansion parameter in such a theory is the Reynolds number (Re); one
needs therefore to perform infinite resummations to change the effective
expansion parameter. We present in detail the Dyson-Wyld line resummation which
allows one to dress the propagators, and to change the effective expansion
parameter from Re to O(1). Next we develop the ``dressed vertex" representation
of the diagrammatic series. Lastly we discuss in full detail the path-integral
formulation of the statistical theory of turbulence, and show that it is
equivalent order by order to the Dyson-Wyld theory. On the basis of the
material presented here one can proceed smoothly to read the recent
developments in this field.
