Prerequisite: Basic courses in complex analysis, ODE, and PDE. Asymptotic approximations, regular and singular asymptotics, approximation of integrals (methods of stationary phase and steepest descents), asymptotic analysis of ODE at regular/irregular singular points, parameter asymptotics for initial/boundary value problems, matched asymptotic expansions, the method of multiple scales, WKB method, weakly nonlinear oscillations and waves, bifurcation and stability.