The solutions of impulsive differential equations (IDEs) are often discontinuous and are not integrable in the ordinary sense of the word as most hypotheses in differential equations normally assumed.This peculiarity makes (IDEs) not easily accessible to most existing concepts and theorems in the differential equations. Therefore the existing concepts, theories in Differential Equations need to be strengthened or new ones developed before applying to (IDEs).This book will be useful to Students and practitioners in the field and in the industry working on problems with impulsive attributes such as modeling/computer simulation of stock price and petroleum pricing, disaster management, harvesting problem, biomedical problems, engineering and so on. We utilized several interesting techniques in nonlinear analysis such as topological degree, compact operators, monotone-iterative technique, measure of non-compact maps, inequalities on cone and applied them to some practical problems including, Numerical approximation of solutions of impulsive differential equations and measure differential equations