The present volume comprises the contributions of some of the participants of the NATO Advance Studies Institute "Turbulence, Weak and Strong", held in Cargese, in August 1994. More than 70 scientists, from seniors to young students, have joined together to discuss and review new (and not so new) ideas and developments in the study of turbulence. One of the objectives of the School was to incorporate, in the same meeting, two aspects of turbulence, which are obviously linked, and which are often treated separately: fully developed turbulence (in two and three dimensions) and weak turbulence (essentially one and two-dimensional systems). Decaying two-dimensional turbulence refers to the solution ot the two-dimensional, incompressible Navier-Stokes equation as an unforced initial value problem. This is an instructive counterpoint to the complementary problem of forced two-dimensional turbulence. In both cases one is concerned with high Reynolds number flows in which inertia dominates the other processes (viscosity and forcing) over many decades of length scales.