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This notebook is intended to give a first introduction to hydrodynamic instability. This includes both the physical concepts and several useful mathematical manipulations. The first chapter discusses the concept of linear instability theory and uses a simple wave equation to demonstrate the linearization and calculation of temporal and spatial growth. The second is an introduction to magnetohydrodynamics. In the chapter 3, we give a brief survey of Beltrami fields and ABC flows. In the chapter 4 we study the stability of the magnetostatic equilibrium through a relaxation of a magnetic field B...