Ultraviolet photometry is presented for the globular cluster M79 (NGC 1904) according to the final calibration of the images obtained on the Astro-1 Spacelab mission by the Ultraviolet Imaging Telescope. These results include both point-source and surface photometry at 152nm and 249nm. An ultraviolet color-magnitude (C-M) diagram in these bandpasses is presented. The detected stars are also cross-matched with the ground-based photometry of Ferraro et al. (1992MNRAS.256..391F) to produce C-M and two-color diagrams covering a 4000A span in wavelength. The observed horizontal branch (HB) is compared with stellar interior models of the zero-age HB (ZAHB). Many stars are found in post-HB evolutionary stages more luminous than the ZAHB. The distribution of stars along the ZAHB in m152-m249 color is investigated, and an indication of possible bimodality is found. The relative population of the blue HB tail may vary with radius for radii greater than 1'. Ultraviolet surface brightness and color-index profiles are presented. The previously reported central gradient in the m152-V color index is confirmed, and a faint diffuse component is detected outside a radius of 40" in the 152nm band. Two possible causes of the central color gradient are discussed: mass segregation, and the destruction of red giant envelopes by enhanced mass loss in the cluster core.