What is Mach number and why is it important in aerodynamics?

Mach number is the ratio of the aircraft's velocity to the local speed of sound (M = V/a). It is crucial because aerodynamic behavior changes significantly across different Mach regimes: subsonic (M < 0.8), transonic (0.8 < M < 1.2), supersonic (1.2 < M < 5), and hypersonic (M > 5). Compressibility effects become significant above Mach 0.3, affecting pressure distributions, drag, and shock wave formation.