Concept of stability of fluid flows. Two types of stability analysis: normal modes method and treating the stability problem as an initial value problem. Linearizing the governing equations. Several instabilities examined in detail: Rayleigh-Taylor, Jeans instability, Rayleigh-Benard convection, Kelvin-Helmholtz instability, Richtmyer-Meshkov instability. Derivation of stability criteria. Parallel shear flows along with derivations of Rayleigh and Orr- Sommerfeld equations and discussion of algebraic growth. Numerical techniques for computationally determining stability including the novel use of numerical inverse Laplace Transforms. Introductory global stability analysis.