This book constitutes the refereed proceedings of the First International Conference on the Foundations of Software Science and Computation Structures, FoSSaCS'98, held as part of the Joint European Conferences on Theory and Practice of Software, ETAPS'98, in Lisbon, Portugal, in March/April 1998. The 19 revised full papers presented in the book were carefully selected from a total of 44 submissions. Among the topics covered are formal specification, automata theory, term rewriting and rewriting systems, process algebras, formal language theory, type theory, event structures, and iteration theory.