Sir Isaac Newton conveyed to the real world the idea of modeling the motion of physical systems with equations. Nearly a hundred years ago it was known that deterministic systems can exhibit very complicated behavior. In the present day, scientists realize that the chaotic behavior can be observed almost in all domains of science and technology. Chaotic world reveals incomprehensibly complex behavior. In this book we have considered mainly some problems of discrete dynamical systems in one dimension. The problems have been selected very carefully. Most (but not all) of the results are pertaining to chaos. Some applications of chaos theory have also been discussed. The purpose of this book is to provide a textbook on discrete 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.