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We consider a model of a D-dimensional tethered manifold interacting byexcluded volume in R^d with a single point. Use of intrinsic distance geometryprovides a rigorous definition of the analytic continuation of the perturbativeexpansion for arbitrary D, 0 < D < 2. Its one-loop renormalizability is firstestablished by direct resummation. A renormalization operation R is thendescribed, which ensures renormalizability to all orders. The similar questionof the renormalizability of the self-avoiding manifold (SAM) Edwards model isthen considered, first at one-loop, then to all orders. We describe ashort-distance multi-local operator product expansion, which extends methods oflocal field theories to a large class of models with non-local singularinteractions. It vindicates the direct renormalization method used earlier inpart I of these lectures, as well as the corresponding scaling laws.Comment: 32 pages, 9 figures, Second Part and extensive update of Lecture  Notes originally given in ``Statistical Mechanics of Membranes and  Surfaces'', Fifth Jerusalem Winter School for Theoretical Physics (1987), D.  R. Nelson, T. Piran,and S. Weinberg ed

STATISTICAL MECHANICS OF SELF-AVOIDING CRUMPLED MANIFOLDS — Part II