We give an overview of the Galaxy Evolution Explorer (GALEX), a NASA Explorer Mission launched on April 28, 2003. GALEX is performing the first space UV sky-survey, including imaging and grism surveys in two bands (1350-1750 Angstroms and 1750-2750 Angstroms). The surveys include an all-sky imaging survey (m[AB] ~ 20.5), a medium imaging survey of 1000 square degrees (m[AB] ~ 23), a deep imaging survey of 100 square degrees (m[AB] ~ 25), and a nearby galaxy survey. Spectroscopic grism surveys (R=100-200) are underway with various depths and sky coverage. Many targets overlap existing or planned surveys. We will use the measured UV properties of local galaxies, along with corollary observations, to calibrate the UV-global star formation rate relationship in local galaxies. We will apply this calibration to distant galaxies discovered in the deep imaging and spectroscopic surveys to map the history of star formation in the universe over the redshift range 0 < z < 1.5, and probe the physical drivers of star formation in galaxies. The GALEX mission includes a Guest Investigator program supporting the wide variety of programs made possible by the first UV sky survey.