The idea of modeling the motion of physical systems with mathematical equations was first conveyed to the real world by Sir Isaac Newton. In the present day, mathematicians realize that the chaotic behavior can be observed almost in every area of science and technology. Any chaotic function exposes inconceivably complicated behavior. In this book we have considered mainly some problems of symbolic dynamical systems, which is a part of discrete dynamical systems. We think that this book is the first one to be written on this particular type of symbol space. The problems which are discussed here are chosen very watchfully. Most of the results which we have discussed here are pertaining to chaos. We also have provided a brief discussion on the origin of dynamical systems. The purpose of this book is to provide a textbook on symbolic dynamical systems for the college or university students and also to help researchers pursuing this line of research. We strongly hope for wide acceptance of the contents of this book.