The theory of Quantum Groups is a rapidly developing areawith numerous applications in mathematics and theoreticalphysics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantumintegrable models. The aim of the Euler Institute’sworkshops was to review and compile the progress achieved inthe different subfields. Near 100 participants came from 14countries. More than 20 contributions written up for thisbook contain new, unpublished material and half of theminclude a survey of recent results in the field (deformationtheory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problemsin Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky, L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.