This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time, the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.