The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable $C^*$-algebras, the Baum-Connes conjecture, $E_0$ semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Minimal $E 0$-semigroups by W. B. Arveson Bimodules, higher relative commutants, and the fusion algebra associated to a subfactor by D. H. Bisch On selfdual Hilbert modules by D. P. Blecher Kunneth splittings and classification of $C^*$-algebras with finitely many ideals by S. Eilers Cut-down method in the inductive limit decomposition of noncommutative tori. II: The degenerate case by G. A. Elliott and Q. Lin A classification of simple limits of dimension drop $C^*$-algebras by G. A. Elliott, G. Gong, X. Jiang, and H. Su Remarks on the Baum-Connes conjecture and Kazhdan's property $T$ by P. Julg Integer groups of coinvariants associated to octagonal tilings by J. Kellendonk On the existence of traces on exact stably projectionless simple $C^*$-algebras by E. Kirchberg Crossed products of Cuntz algebras by quasi-free automorphisms by A. Kishimoto and A. Kumjian Almost commuting selfadjoint matrices and applications by H. Lin Real rank of multiplier algebras of $C^*$-algebras of real rank zero by H. Lin and H. Osaka Approximate unitary equivalence of homomorphisms from odd Cuntz algebras by N. C. Phillips Classification of certain infinite simple $C^*$-algebras. III by M. Rordam KMS states and phase transitions. II by S. Sakai Asymnptotic morphisms and $E$-theory by J. N. Samuel Representing $K 1$ in the unitary group by K. Thomsen.