Probabilistic Models for Nonlinear Partial Differential Equations : Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme Italy May 22–30 1995 The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDEs and their Numerical Applications (April 1995) had a three fold emphasis: first on the weak convergence of stochastic integrals; second on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws Boltzmann like and Navier Stokes equations); third on the modelling of networks by interacting particle systems. This book collecting the notes of these courses will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs in particular to PhD students and young researchers