Scientists, as also Mathematicians, universally preserve an eternal desire to reveal nature''s unifying laws and fashion them with a comfortable language in order to further the progress of human knowledge. The theory of dynamical systems, describing phenomena common to both physical and biological systems, has been developed from the collision of ideas of Mathematicians, and physical and biological Scientists. Discrete dynamical systems, a special class of dynamical systems, evolved as a discipline of science and in particular of mathematics during the last five decades of twentieth century, have many facets, pioneered by some eminent Mathematicians. This book deals with some aspects of non-linear dynamical systems, especially chaotic dynamical systems, has examined critically few areas of the systems vis-à- vis some already established theories and advocated new theories. The analysis should especially encourage the researchers and Mathematicians involved in in-depth study of this interesting system.