[en] Hypernuclear spectroscopy study via the (e,e'K+) reaction has been carried out for the first time, establishing a new technique to study Lambda hypernuclei. The high quality electron beam at Jefferson Lab made it possible to measure Lambda hypernuclear spectra with an energy resolution better than 1 MeV (FWHM). The present experiment was designed to make full use of the virtual photon flux, which peaks at very forward angles, by detecting scattered electrons at 0 degrees. Scattered positive kaons were also detected near 0 degrees, where the cross section of the kaon photo-production is maximized. This unique kinematical configuration was realized with the HyperNuclear Spectrometer System (HNSS), which consisted of the Short-Orbit Spectrometer, the Enge Split-Pole Spectrometer, and the splitter magnet. The Lambda12B mass spectrum was measured in the 12C(e,e'K+)Lambda12B reaction with 0.9 MeV (FWHM) energy resolution. The averaged binding energy of the Lambda12B ground state doublet was obtained to be 11.7 ± 0.1 (statistical) ± 0.3 (systematic) MeV, which is consistent with emulsion data. The general spectral structure of the 12C(e,e'K+) Lambda12B reaction was found to be similar to that of the 12C(Lambda+,K+)Lambda12C reaction, showing characteristic peaks corresponding to sLambda and pLambda orbits, as well as a few core-excited states. The cross section of the Lambda12B ground state doublet was derived to be 117 ± 13 (statistical) ± 14 (systematic) nb/sr. The theoretical prediction of the cross section was consistent with the present result, validating DWIA calculation for hypernuclear yields. The present study proved the effectiveness of the (e,e'K+) reaction for future Lambda hypernuclear spectroscopy studies