The author presents a topological approach to the problem of robustness of dynamic feedback control. First the gap-topology is introduced as a distance measure between systems. In this topology, stability of the closed loop system is a robust property. Furthermore, it is possible to solve the problem of optimally robust control in this setting. The book can be divided into two parts. The first chapters form an introduction to the topological approach towards robust stabilization. Although of theoretical nature, only general mathematical knowledge is required from the reader. The second part is devoted to compensator design. Several algorithms for computing an optimally robust controller in the gap-topology are presented and worked out. Therefore we hope that the book will not only be of interest to theoreticians, but that also practitioners will benefit from it.