Control of Partial Differential Equations : Cetraro Italy 2010 Editors: Piermarco Cannarsa Jean Michel Coron The term “control theory” refers to the body of results theoretical numerical and algorithmic which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS Italy) July 19 23 2010. Specifically it covers the stabilization of evolution equations control of the Liouville equation control in fluid mechanics control and numerics for the wave equation and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field representing at the same time a friendly introduction to and an updated account of some of the most active trends in current research. 1 On some recent advances on stabilization for hyperbolic equations 2 Notes on the Control of the Liouville Equation 3 Some questions of control in ﬂuid mechanics 4 Carleman estimates and some applications to control theory 5 The Wave Equation: Control and Numerics.