This two-volume work serves a double purpose， roughly（but not entirely） corresponding to the division into volumes. The first purpose（which occupies Volume 1 and part of Volume 2） is to provide a leisurely introduction to the basic functional analysis underlying the theory of infinitedimensional unitary representations of locally compact groups and its generalization to representations of Banach algebras. Thus， the first volume covers generally well-known material on measure theory（Chapter II）， topological groups and their group algebras（Chapter III）， purely algebraic representation theory（Chapter IV）， Banach algebras（Chapter V）， C*-algebras and their *-representations（Chapter VI）， and the topology of *-representations（Chapter VII）. Chapters IX and X（in Volume 2）， which deal mostly with classical material on compact groups and locally compact Abelian groups respectively， also serve primarily the first purpose.
　　The second purpose（which occupies Chapters VIII， XI， and XII of Volume 2） is to bring the reader to the frontiers of present-day knowledge in one limited but important area， namely， the Mackey normal subgroup analysis and its generalization to the context of Banach *-algebraic bundles. Here too our presentation is quite leisurely. Chapter VIII deals with Banach *-algebraic bundles and their representations.