• Introduction on the astrophysical gas, ISM in particular
• Ideal fluids: Fluid approximation; Continuity and Euler equations; Equation of state: barotropic, adiabatic and isothermal flows; Energy equation; Heat sources: conduction and radiation; Entropy and heat equation; Propagation of sound waves, sound speed.
• Hydrostatic equilibrium: Isothermal sphere; X-ray emitting gas in galaxy clusters; Isothermal slab; Thickness of galaxy discs.
• Supersonic Flow: Mach number; Shock waves; Rankine-Hugoniot jump conditions; Entropy jump; Radiative shocks; Evolution of a supernova remnant.
• Hydrodynamic Instabilities: Convection, Kelvin-Helmholtz, Rayleigh Taylor, Gravitational and Thermal.
• Viscous fluids: Momentum flux and stress tensor; Viscous stress tensor; Navier-Stokes equation; Kelvin circulation theorem; Vorticity in viscous fluids; Energy dissipation in viscous flows; General heat equation.
• Turbulence: Reynolds number; Transition to turbulence in a Poiseuille flow; Fully developed turbulence, Kolmogorov law; Compressible turbulence, sources of turbulence in the ISM.
• Introduction to MHD: Charge neutrality, infinite conductivity; Field freezing; Euler equation with magnetic force; Magnetic Pressure and tension; Magnetic virial theorem; Hydromagnetic waves; Shocks with magnetic field.