From a modelling point of view, it is realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time-scale or measure chain. TTherefore the question can be asked as to whether it is possible to provide a framework which permits handling of both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. This book presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we dynamic systems on time scales and prove the basic properties of solutions of such dynamic systemsare introduced. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the work are that it demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework and it provides an impetus to investigate in the set p of time scales other important problems which might offer a better understanding of the intricacies of a unified study.