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There were many developments in the area of knot theory in the 1990s. They include Thurston's work on geometric structures on 3-manifolds (such as knot complements), Gordon-Luecke's work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones' ideas and Thurston's idea are connected with the following path: hyperbolic structures, PSL(2,C) representations, character varieties, quantization of the co-ordinate ring of the variety to skein modules (such as Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those topics.