This lecture covers dynamic boundary conditions in fluid mechanics, focusing on the relationship between velocity and normal vectors, as well as the implications of different curvatures on fluid stability. It also delves into perturbation and linearization techniques, base state assumptions, and normal mode expansions. The instructor discusses Laplace equations, Euler equations, and the dispersion relation to analyze fluid flow stability. The lecture concludes with a study of surface tension effects and the destabilization of fluid jets.