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Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.

C*-algebras. --- Hilbert algebras. --- Algebras, Hilbert --- Functional analysis --- Von Neumann algebras --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Hilbert modules. --- Modules (Algebra) --- C*-algebras --- Hilbert modules --- Algebra