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This volume attempts to give a comprehensive discussion of the theory of operator algebras (C*-algebras and von Neumann algebras. ) The volume is intended to serve two purposes: to record the standard theory in the Encyc- pedia of Mathematics, and to serve as an introduction and standard reference for the specialized volumes in the series on current research topics in the subject. Since there are already numerous excellent treatises on various aspects of thesubject,howdoesthisvolumemakeasigni?cantadditiontotheliterature, and how does it difier from the other books in the subject? In short, why another book on operator algebras? The answer lies partly in the first paragraph above. More importantly, no other single reference covers all or even almost all of the material in this volume.