Distributed parameter systems are described by partial differential equations. They are ``singular'' when the considered equations are unstable or when they have multiple solutions (such as bifurcations) or when there is no solution. The control of such systems is an important problem in several domains, for example biochemical processes, plasmas, transport of electrical energy, etc. This book presents the theoretical principles of singular systems. The optimality system in the singular case is considered as a generalization of the nonsingular case. It seems that, in both cases, the structure of the optimality system is the same. In this book, the author presents cases for which the optimality system is known, for stationary problems with multiple solutions and for nonlinear unstable problems, as well as ill-conditioned problems