This thesis describes the design and testing of a high gradient RF cavity for the muon cooling channel of the muon collider. The 805 MHz multi-cell open iris cavity was high power tested with a 12 MW klystron in a superconducting solenoid environment. The cavity reached 21 MV/m for peak klystron power in the absence of the solenoidal field. During magnetic field operation, the cavity suffered serious surface damage and RF breakdown. Dark current in excess of 400 mA was observed. Present R & D results imply that the cavity is not suitable for the muon collider. To my parents, with profound gratitude. As with any experimental effort, many people have contributed to the successful completion of this project. My foremost thank goes to my thesis advisors Randy Johnson and Norbert Holtkamp for their constant support and guidance throughout my thesis research. Next, I would like to thank Al Moretti, Derun Li, Zubao Qian, Tom Jurgens and Mark Champion for whom I have learned a great deal about the design and testing of RF cavity. They were always there to help when I needed them. I thank Steve Geer (MUCOOL spokesperson) and Norbert Holtkamp for their relentless support of the project which kept the project alive during times of Fermilab budgetary cuts.