This presentation contains notes for a one-hour lecture that is part of a two-day AIAA Short Course titled, Hypersonic Air-Breathing Propulsion: Emerging Technologies and Cycles. The presentation covers an introduction to Pressure Gain Combustion (PGC) and its applicability to high speed airbreathing propulsion (HSABP). The concept of PGC is discussed on a thermodynamic basis, the performance benefits are demonstrated, and methods of implementation are described. These include devices such as Resonant Pulse Combustors, Internal Combustion Wave Rotors, Pulse Detonation Engines, and Rotating Detonation Engines.