These Proceedings comprise the bulk of the papers presented at the Inter- national Conference on Semigroups of Opemtors: Theory and Contro held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the- ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab- stract theory and the applications and one of the Conference aims was to bring together...