Extrasolar planets orbiting M-stars may represent our best chance to discover habitable worlds in the coming decade. The ultraviolet spectrum incident upon both Earth-like and Jovian planets is critically important for proper modeling of their atmospheric heating and chemistry. In order to provide more realistic inputs for atmospheric models of planets orbiting low-mass stars, we present new near- and far-ultraviolet (NUV and FUV) spectroscopy of the M-dwarf exoplanet host GJ 876 (M4V). Using the COS and STIS spectrographs on board the Hubble Space Telescope, we have measured the 1150-3140 Å spectrum of GJ 876. We have reconstructed the stellar H I Lyα emission line profile, and find that the integrated Lyα flux is roughly equal to the rest of the integrated flux (1150-1210 Å + 1220-3140 Å) in the entire ultraviolet bandpass (F(Lyα)/F(FUV+NUV) 0.7). This ratio is ~2500× greater than the solar value. We describe the ultraviolet line spectrum and report surprisingly strong fluorescent emission from hot H₂ (T(H₂) > 2000 K). We show the light curve of a chromospheric + transition region flare observed in several far-UV emission lines, with flare/quiescent flux ratios ≥10. The strong FUV radiation field of an M-star (and specifically Lyα) is important for determining the abundance of O₂—and the formation of biomarkers—in the lower atmospheres of Earth-like planets in the habitable zones of low-mass stars.