The results of experimental and theoretical investigations of the photodissociation XeF laser operating in the visible and UV regions and pumped by the radiation of an open discharge initiated by an electric explosion of thin metal wires are reported. A detailed description of the laser design and experimental techniques is given. The analysis of the energy balance in the XeF laser on the basis of measurements of energetic parameters of laser radiation and the pump source are performed. The results of optical investigations of the active medium aimed at the study of the interaction of high-power fluxes of pump radiation with the absorbing active medium are presented. This interaction forms free-running bleaching and inversion waves in the active medium. Spectral, spatial, time, and energy characteristics of laser radiation on the B-X({lambda} = 353 nm) and C-A({lambda} = 480 nm) transitions of XeF are investigated. The instantaneous laser efficiency with respect to the electrical power feeding the pump source is shown to be about 1%. The specific energy of laser radiation on the C-A transition in the blue-green region was 8.5 J/liter for a total laser energy of 14.5 J. The specific energy of radiation on the B-X transition in the UV region was 16.5 J/liter for a total energy of 28 J. Kinetic models of the optically pumped XeF laser describing its operation on both transitions are developed. They allow calculations of unsaturated gain, output energy, and laser efficiency.