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This IFIP state-of-the-art report presents a collection of fundamental high-quality contributions on the algebraic foundations of systems specification. The contributions cover and survey current topics and recent advances, and address such subjects as: the role of formal specification, algebraic preliminaries, partiality, institutions, specification semantics, structuring, refinement, specification languages, term rewriting, deduction and proof systems, object specification, concurrency, and the development process. The authors are well-known experts in the field. The book is an outcome of IFIP WG 1.3 (Foundations of Systems Specification) in cooperation with Esprit Basic Research WG COMPASS, and provides the foundations of the algebraic specification language CASL designed in the CoFI (Common Framework Initiative for Algebraic Specification and Development) project. It is aimed at system developers, researchers, and students.