Introduction to Nonlinear Systems. Multiple equilibria, limit cycles, bifurcations, chaos. Examples from physics and engineering. Lyapunov exponents. Index theorem. Poincare, Poincare Bendixson, Liouville Theorems. Recurrence. Describing functions. Stability. Theorems of Lyapunov, La Salle, Chetaev. Popov and Circle criteria. Kalman Yakubovich Lemma, Passivity. Feedback Linearization. Lie brackets. Frobenius Theorem. Adaptive Control: Model Reference, Self Tuning. Several Techniques for Nonlinear Control Design: Stabilization via Linearization, Integral Control, Backstepping, Lyapunov Redesign, Gain Scheduling. Introduction to Chaos.