This course studies control synthesis for 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 (CLF), and corresponding stabilization results in the context of optimization-based controllers. This leads to control barrier functions (CBFs), which enforce safety on nonlinear systems via safety filters. The interplay between stability (CLFs) and safety (CBFs) will be studied from a variety of perspectives. Advanced topics that build upon these core results will be discussed, including: robust, adaptive and event-triggered control, layered control architectures, model-predictive control and hybrid systems. The control of robotic systems will be used as a motivating example.