1 Introduction and General Results. - 1. 1 Introduction. - 1. 2 Nonlinear Disturbance Equations. - 1. 3 Definition of Stability and Critical Reynolds Numbers. - 1. 4 The Reynolds-Orr Equation. - I Temporal Stability of Parallel Shear Flows. - 2 Linear Inviscid Analysis. - 3 Eigensolutions to the Viscous Problem. - 4 The Viscous Initial Value Problem. - 5 Nonlinear Stability. - II Stability of Complex Flows and Transition. - 6 Temporal Stability of Complex Flows. - 7 Growth of Disturbances in Space. - 8 Secondary Instability. - 9 Transition to Turbulence. - III Appendix. - A Numerical Issues and Computer Programs. - A. 1 Global versus Local Methods. - A. 2 Runge-Kutta Methods. - A. 3 Chebyshev Expansions. - A. 4 Infinite Domain and Continuous Spectrum. - A. 5 Chebyshev Discretization of the Orr-Sommerfeld Equation. - A. 6 MATLAB Codes for Hydrodynamic Stability Calculations. - A. 7 Eigenvalues of Parallel Shear Flows. - B Resonances and Degeneracies. - B. 1 Resonances and Degeneracies. - B. 2 Orr-Sommerfeld-Squire Resonance. - C Adjoint of the Linearized Boundary Layer Equation. - C. 1 Adjoint of the Linearized Boundary Layer Equation. - D Selected Problems on Part I. Language: English