This course studies nonlinear control systems from Lyapunov perspective. Beginning with feedback linearization and the stabilization of feedback linearizable system, these concepts are related to control Lyapunov functions, and corresponding stabilization results in the context of optimization based controllers. Advanced topics that build upon these core results will be discussed including: stability of periodic orbits, controller synthesis through virtual constraints, safety-critical controllers, and the role of physical constraints and actuator limits. The control of robotic systems will be used as a motivating example.