This text emphasizes the use of algebraic methods and techniques in the study of operators and their applications. It includes carefully selected articles aimed at bridging dfferent, but related, areas of mathematics which have only recently displayed unexpected interconnections, as well as new cross-fertilizations. The articles have been grouped into chapters on single operators and applications, non-selfadjoint algebras, C-algebras, von Neumann algebras and subfactors, representation of groups and algebras on Hilbert space, and geometry and topology. This has been done in an effort to stress the complementarity between diversity of topics on one hand, and unity of ideas on the other.