Subfactors, a subject of considerable research activity for about fifteen years, are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. The authors present a new pictorial approach to subfactors in addition to discussions of basic principles. This book provides an important introduction to the subject and is aimed at students with only a little familiarity with the theory of Hilbert space and other newcomers to the field.

1. Factors; 2. Subfactors and index; 3. Some basic facts; 4. The principal and dual graphs; 5. Commuting squares; 6. Vertex and spin models.