A mosaic of four UIT far-UV (FUV; 1620A) images, which covers most of the SMC bar, is presented, with derived stellar and HII region photometry. The UV morphology of the Bar shows that recent star formation there has left striking features including: a) four concentrations of UV-bright stars spread from northeast to southwest at nearly equal (~30 arcmin=0.5 kpc) spacings; b) a well-defined 8-arcmin ring of UV-bright stars surrounded by a larger H-alpha ring, suggesting sequential star formation. FUV PSF photometry is obtained for 11,306 stars, and a FUV luminosity function is derived. A (FUV-V,V) color-magnitude diagram for 195 identified supergiants, with derived extinctions; the bluest (least-reddened) stars of each spectral type have FUV-V colors consistent with models. FUV photometry is obtained for 42 H-alpha-selected HII regions, both for the stars and for the total emission within the apertures defined by Kennicutt & Hodge. The flux-weighted average ratio of total to stellar FUV flux is 2.15; the stellar FUV luminosity function indicates that most of the excess total flux is due to scattered FUV radiation, rather than faint stars. Both stellar and total emission are well correlated with H-alpha fluxes, and yield FUV/H-alpha ratios that are consistent with models of single-burst clusters with SMC metallicity, ages from 1-5 Myr, and moderate (E(B-V)=0.0-0.1 mag) internal SMC extinction.