A system in which a function describes the time dependence of a point in a geometrical space is referred to as a dynamical system. The mathematical models that describe the swinging of a clock pendulum, the number of fish present each springtime in a lake and the flow of water in a pipe are some of the examples of dynamical systems. A domain of mathematics that is used to describe the behavior of complex dynamical systems by using differential equations is referred to as dynamical systems theory. The focus of dynamical systems theory is the study of dynamical systems which has applications in a wide variety of fields such as mathematics, physics, chemistry, biology, engineering, economics, history and medicine. Dynamical systems are a crucial part of logistic map dynamics, chaos theory, bifurcation theory, the self-assembly and self-organization processes, and the edge of chaos concept. This book brings forth some of the most innovative concepts and elucidates the unexplored aspects of dynamical systems. Its aim is to present researches that have transformed this discipline and aided its advancement. This book will serve as a reference to a broad spectrum of readers.