Dynamical system is the branch of mechanics concerned with the motion/changes of bodies/systems under the action of forces. The acting forces are not in equilibrium. The branch of any science in which changes in variables are considered e.g. chemical kinetics, population biology, nonlinear oscillations, econophysics, etc. All these subjects can be placed under this common mathematical framework. Nonlinear dynamical systems concern with dynamical systems or processes that are inherently nonlinear. These systems describe changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. In thiscourse, we will study Nonlinearity Dynamical Systems. The topics that we will cover include: Nonlinear dynamic systems, from periodic to chaotic systems; Classification and characteristics of Nonlinear mathematical models; Other deterministic chaotic systems (maps, feedback loops).