This lecture discusses the mechanism and analysis of centrifugal instabilities, focusing on the Rayleigh criterion for stability, experimental setups using a 'Coriolis' rotating platform, anticyclones, cyclones, Navier-Stokes equations, base flow analysis, viscous and convective times, and the comparison between theory and experiments. It also covers the Rayleigh criterion's general solution, conditions for instability, wall-bounded flows, comparison between theory and experiment, backward facing step analysis, global dispersion relations, and Gortler instability.