This seminar, organized by Man-Duen Choi, Chandler Davis, George Elliott, and Peter Rosenthal, is devoted, loosely speaking, to the study of all areas of mathematics involving Hilbert space operators. (This has variously been interpreted recently to include matrix theory, index theory of differential operators and other aspects of non-commutative geometry, invariant subspace theory, quantum information theory, C*-algebra classification theory, and string theory.)