This book constitutes the refereed proceedings of the First International Workshop on Hybrid Systems: Computation and Control, held in Berkeley, California, USA, in April 1998. The volume presents 27 revised full papers selected from a total of 55 submissions. The papers focus on mathematical methods for the rigorous and systematic design and analysis of hybrid systems. Hybrid systems consist of digital devices that interact with analog environments; they are particularly important in context with safety-critical systems and dependable computing. The present volume extends the line of hybrid systems research documented in volumes 736, 999, 1066, 1201, and 1273 of the LNCS series.