This monograph extends Realization Theory to the discrete-time domain. It includes new results and constructs a new and very wide inclusion relation for various non-linear dynamical systems. After establishing some features of discrete-time dynamical systems it presents results concerning systems which are proposed by the authors for the first time. They introduce General Dynamical Systems, Linear Representation Systems, Affine Dynamical Systems, Pseudo Linear Systems, Almost Linear Systems and So-called Linear Systems for discrete-time and demonstrate the relationship between them and the other dynamical systems. This book is intended for graduate students and researchers who study control theory.