This lecture covers the theory of Prandtl-Meyer flows, focusing on speed variations, infinitesimal changes across Mach lines, and the Prandtl-Meyer function. It explains the tangential speed constancy across Mach lines and the analytical derivation of the Prandtl-Meyer function. The lecture also discusses the utilization of the function for isentropic compression and relaxation waves, highlighting its significance in representing flow angles. Additionally, it explores the interpretation of the Prandtl-Meyer function and its role in ramping flow from Mach 1. The content is supported by slides from the Federal Institute of Lausanne and the Polytechnic University.