“…As can be seen in the set of lectures in this volume, which presents an extended version of [1], the statistical mechanics of random surfaces and membranes, or more generally of extended objects, poses fundamental problems. The study of polymerized membranes, which are generalizations of linear polymers [2,3] to two-dimensionally connected networks, is emphasized, with a number of possible experimental realizations [4,5,6,7,8], or numerical simulations [9,10]. From a theoretical point of view, a clear challenge in the late eighties was to understand self-avoidance (SA) effects in membranes.…”