Fundamentals and modeling of reacting gas dynamics and combustion using analytical and numerical methods. Conservation equations of reacting flows. Multi-species transport, chemical thermodynamics and chemical kinetics. Non-equilibrium flow. Detonation and reacting boundary layers. Ignition, flammability, and extinction. Premixed and diffusion flames. Combustion instabilities. Supersonic combustion. Turbulent combustion. Liquid and solid burning. Fire, safety, and environmental impact. Applications to power and propulsion.