Plasma railguns are electromagnetic accelerators used to produce controlled high velocity plasma jets. This thesis discusses the design and characterization of a small coaxial plasma railgun intended to accelerate argon-helium plasma jets. The railgun will be used for the study of plasma shocks in jet collisions. The railgun is mounted on a KF-40 vacuum port and operated using a 90 kA, 11 kV LC pulse forming network. Existing knowledge of coaxial railgun plasma instabilities and material interactions at vacuum and plasma interfaces are applied to the design. The design of individual gun components is detailed. Jet velocity and density are characterized by analyzing diagnostic data collected from a Rogowski coil, interferometer, and photodiode. Peak line-integrated electron number densities of approximately 8 × 10¹⁵ cm^-2 and jet velocities of tens of km/s are inferred from the data recorded from ten experimental pulses. / Master of Science / Plasma is a gaseous state of matter which is electrically conductive and interacts with electric and magnetic fields. Plasmas are used in many everyday objects such as fluorescent lights, but some of the physics of plasmas are still not entirely understood. One set of plasma interactions that have not been fully explored are those which occur during high-velocity collisions between plasmas. Experiments aimed to further the understanding of these interactions require the generation of plasmas with specified properties at very high velocities. A device known as a plasma railgun can be used to produce plasmas which meet these experimental demands. In a plasma railgun, a short pulse of current is passed through a plasma located between two parallel electrodes, or "rails". This current generates a magnetic field which propels the plasma forward. The plasma is accelerated until it leaves the muzzle of the railgun. In coaxial plasma railguns, the electrodes are concentric. This paper discusses the design and testing of a small, relatively low power coaxial plasma railgun. Specific elements of the design are examined and the inherent physical and material difficulties of a coaxial design are explored. The experiment which was performed to confirm the properties of the plasma jets produced by the coaxial plasma railgun is explained. The results of this experiment confirm that the design succeeds in producing plasmas which meet targets for plasma properties.