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Quantum symmetries modelled through quantum groups or their duals, quantum algebras, is a very active field of relevant physical and one and with promising physical applications. This volume gives some information on the progress of this field during the years after the quantum group workshop in Clausthal, 1989. Quantum symmetries are connected with very different approaches and views. The field is not yet coherent; there are different notions of quantum groups and of quantum algebras through algebraic deformations of groups and algebras. Hence its development has various directions following more special mathematical and physical interests.