Chaos is a property of dynamical system which is completely unordered, unpredictable, uncontrolled and has a sensitive dependence on initial condition as the main features of chaos. This book presents some analyses on chaotic dynamical systems. We study on the findings of the critical values formula for the chaotic system by using the linearized system and characteristic equations for chaotic dynamical flows. Some numerical methods are used to solve the chaotic systems for maps and flows. We also investigate about the sensitivity to initial conditions which is measured by the Lyapunov...