This book focuses on an area of approximations in applied mathematics known as asymptotic analysis and perturbation theory and the relatively new and powerful technique - multiple scales theory - that rests on these theories. This new theory has been applied to a large number of diverse advanced engineering systems. Engineering analysts and designers will benefit from the simplicity of the concept and applicability of the method. This book is intended to bridge the gap between esoteric mathematical theory and practical, real world applications. The book is organized into six parts. Part I presents the basic concept, foundations, and the techniques of asymptotic analysis, perturbation theory, and multiple scales. Part II treats the important areas of linear systems by the multiple scales theory. Part III covers the basic ideas governing the dynamics of flight vehicles in the atmosphere and in space. Part IV discusses aircraft applications operating within the earth's atmosphere. Space flight applications are presented in Part V, and Part VI presents some related but separate topics in appendices.