This new and important book expands the idea of the wide spectre of the theory of impulsive equations to the theoretical and applied researchers in mathematics and provides them a tool and motivation for deeper investigations and applications of these equations to real world problems. It deals with the theory of impulsive differential equations, which is a relatively new area and seems to hold a considerable potential. This field started gaining interest around 1980 and today we have several hundred researches working in it and a couple of thousand publications. Many of the theoretical results obtained in the field of impulsive differential equations have already been used in the process of modelling and investigating the properties of real life processes in the sciences and technologies.