The process of electron emission from 30 MeV neutrino absorption on carbon, C12( e,e-)12N, has been observed. The flux-weighted total cross section for the exclusive neutrino-induced nuclear transition C12( e,e-)12N(g.s.) is [1.05 0.10(stat) 0.10(syst)]×10-41 cm2. The measured cross section and angular distribution d /d are in agreement with theoretical estimates. The inclusive e C12 reaction rate, which accounted for the majority of all neutrino interactions observed in this experiment, was determined from a detailed fit of energy and angular distributions for the observed electrons. The inclusive C12( e,e-)X cross section is measured to be [1.41 0.23(tot)]×10-41 cm2. An upper limit for the sum of the C13( e,e-)X+27Al( e,e-)X inclusive absorption cross sections is presented.