Thus, when the authors of the present monograph decided to start the work they were confronted with a very rich literature on the subject. However two reasons motivated their initiative. The first concerns the theory in which the whole development of the book was embedded. As is well known, there are several ways of approach­ oo ing H and robust control theory. Here we mention three relevant direc­ tions chronologically ordered: a) the first makes use of a generalization of the Beurling-Lax theorem to Krein spaces; b) the second makes use of a generalization of Nevanlinna-Pick interpolation theory and commutant lifting theorem; c) the third, and probably the most attractive from an el­ evate engineering viewpoint, is the two Riccati equations based approach which offers a complete solution in state space form.