This ERGEBNISSE volume provides a comprehensive and detailed account of the research in the field of quantum groups. The book is a sequel to J. Dixmier: "Algebres enveloppantes", Gauthier-Villars 1974 and J.-C. Jantzen: "Einhüllende Algebren halbeinfacher Lie-Algebren", Springer-Verlag 1983. It is an important reference work for graduate students and researchers in algebra, the theory of Lie algebras, mathematical physics.