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In 1969, J.L. Lions published his famous book on the control of partial differential equations and paved the way for a rapid development of control theory. The talk introduces in this eld and provides some mathematical techniques that are important for understanding the main techniques and their applicability. Several real applications are addressed, in particular the optimal cooling of milled steel proles, ow measurement by controlled magnetic elds, and the control of traveling wave fronts and spiral waves. Various numerical examples are shown.