The Extreme Ultraviolet Explorer mission is described. For the first six months, an all-sky survey will be carried out covering 90 to 750 Å, or essentially the entire extreme ultraviolet (EUV) bandpass. This EUV survey will be made in four bands, or colors: λλ 90-150 Å, 170-250 Å, 400-600 Å, and 550-750 Å. A portion of the sky which is free from the normally intense 304 Å geocoronal helium background will be surveyed at greater sensitivity; the wavelength coverage of this band is from 90 to 400 Å. Following the sky survey portion of the mission, spectroscopy of individual sources will be carried out. Three spectrometers employing novel variable line-space gratings will provide spectra with ~1 Å resolution over the band from 70 to 760 Å. This spectroscopy will be carried out by guest observers chosen by NASA in a manner roughly analogous to the International Ultraviolet Explorer (IUE) guest observer program.