It must be stated at the outset that this little monograph has no pretensions to being a general all-purpose text in operator algebras. On the contrary, it is an attempt to introduce the potentially interested reader – be it a graduate student or a working mathematician who is not necessarily an operator algebraist – to a selection of topics in the theory of subfactors, this selection being influenced by the authors' tastes and personal viewpoints. For instance, we restrict ourselves to the theory of (usually hyperfinite) II1 factors and their subfactors (almost always of finite index); thus, factors of type III do not make an appearance beyond the first (introductory) chapter, and the Tomita–Takesaki theorem makes only a cameo appearance in the appendix. It is hoped that such ‘simplifications’ will help to make the material more accessible to the uninitiated reader.

The aim of this book is to give an introduction to some of the beautiful ideas and results which have been developed, since the inception of the theory of subfactors, by such mathematicians as Adrian Ocneanu and Sorin Popa; an attempt has been made to keep the material as self-contained as possible; in fact, we feel it should be possible to use this monograph as the basis of a two-semester course to second year graduate students with a minimal background in Hilbert space theory.