The objective of this course is to equip students with modern tools to analyze and predict the behavior of nonlinear dynamical systems—oscillations, limit cycles, and stability—using time-domain (Lyapunov/LaSalle), frequency-domain (describing functions; Popov, circle/parabola criteria), and perturbation/approximation methods (multiple scales, Poincaré–Lindstedt, Krylov–Bogoliubov). Emphasis is on modeling, rigorous analysis, and simulation-driven insight for engineering systems.