In a collaborative effort by SSRL, AET Associates, and Varian Associates, a high-brightness microwave electron gun using a thermionic cathode has been designed, built, tested, and installed for use with the SSRL 150 MeV linear accelerator. This thesis discusses the physics behind the design and operation of the gun and associated systems, presenting predictions and experimental tests of the gun`s performance. The microwave gun concept is of increasing interest due to its promise of providing higher-current, lower-emittance electron beams than possible from conventional, DC gun technology. In a DC guns, accelerating gradients are less than 8 MV/m, while those in a microwave gun can exceed 100 MV/m, providing much more rapid initial acceleration, thereby reducing the deleterious effects of space-charge. Microwave guns produce higher momentum beams than DC guns, thus lessening space-charge effects during subsequent beam transport. Typical DC guns produce kinetic energies of 80--400 KeV, compared to 2--3 MeV for the SSRL microwave gun. ``State-of-the-art`` microwave gun designs employ laser-driven photocathodes, providing excellent performance but with greater complexity and monetary costs. A thermionic microwave gun with a magnetic bunching system is comparable in cost and complexity to a conventional system, but provides performance that is orders of magnitude better. …