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In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications in both pure mathematics and mathematical physics. The theory was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughn Jones of subfactor theory, leading to remarkable connections with knot theory, 3manifolds, quantum groups, and integrable systems in statistical mechanics and conformal field theory. This book, one of the first in the area, looks at these combinatorialalgebraic developments from the perspective of operator algebras. With minimal prerequisites from classical theory, it brings the reader to the forefront of research.
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