This book lays the foundations of gas- and fluid dynamics. The basic equations are developed from first principles, building on the (assumed) knowledge of Classical Mechanics. This leads to the discussion of the mathematical properties of flows, conservation laws, perturbation analysis, waves and shocks. Most of the discussion centers on ideal (frictionless) fluids and gases. Viscous flows are discussed when considering flows around obstacles and shocks. Many of the examples used to illustrate various processes come from astrophysics and geophysical phenomena.