This book, together with Fundamentals of the Theory of Operator Algebras. Volume II, Advanced Theory, Graduate Studies in Mathematics, vol. 16, present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences.

The book is intended for graduate students and research mathematicians, and mathematical physicists interested in functional analysis, operator algebras, and applications. It can also be used as a text for a graduate course in any of these areas.

Praise for both volumes …

… these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory.

—Bulletin of the London Mathematical Society

Volumes I and II were published in 1982 and 1983. Since then they have quickly established themselves as The Textbooks in operator algebra theory.

—Bulletin of the American Mathematical Society

One of the splendid features of the original two volumes is their large supply of exercises … which illustrate the results of the text and expand its scope.

—L'Enseignement mathématique

Readership

Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.