Laminar-stability theory as a guide to laminar-turbulent transition. Rayleigh equation, instability criteria and response to small inviscid disturbances. Discussion of Kelvin-Helmholtz, Rayleigh-Taylor, Richtmyer-Meshkov and other instabilities, for example, in geophysical flows. The Orr-Sommerfeld equation, the dual role of viscosity, and boundary-layer stability. Modern concepts such as pseudo-momentum conservation laws and nonlinear stability theorems for 2-D and geophysical flows.