This book contains Hurwitz's seminal paper and describes its impact on the development of stability theory and other fields. The major emphasis, however, is on modern developments and applications in the theory of control and numerics. Stability of linear and nonlinear problems, time-dependent systems, discretizations of ordinary and partial differential equations, systems with time delay and multi- dimensional systems are given special attention. In addition, robust stability, pole placement and problems related to the stability radius are considered. This book is of interest to mathematicians and engineers working in the area of control theory and numerics.