SPDE in Hydrodynamic: Recent Progress and Prospects : Lectures given at the C.I.M.E. Summer School held in Cetraro Italy August 29–September 3 2005 Some Methods of Infinite Dimensional Analysis in Hydrodynamics: An Introduction An Introduction to 3D Stochastic Fluid Dynamics Mathematical Results Related to the Navier–Stokes System. Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume the first due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course Franco Flandoli starts from 3D Navier Stokes equations and ends with turbulence. Finally Yakov Sinai in the 3rd course describes some rigorous mathematical results for multidimensional Navier Stokes systems and some recent results on the one dimensional Burgers equation with random forcing.