A positive identification of the minerals olivine, plagioclase, and several types of pyroxenes were made at several locations on the lunar surface by using remote measurements. For example, the crater Aristarchus is found to have an average pyroxene composition of augite, and plagioclase is obviously present. A dark mantle deposit in the crater J. Herschel is at least partly composed of a mixture of 70% olivine and 30% pyroxene. These determinations were possible because the reflectance spectra for 10--20 km diameter lunar areas have been measured for the first time in the IR spectral region (0.65--2.5 μm) with sufficient spectral resolution and photometric precision to define mineral electronic absorption bands. The reflectance for all lunar regions observed (over 100 to present) continues to increase toward longer wavelengths to at least 2.5 μm, and several mineral absorption bands appear. The telescopic spectra are of similar quality and contain features similar to laboratory spectra of lunar samples. The absorption features in several spectra have been quantitatively analyzed using newly developed computer processing techniques, including thermal flux removal and absorption band fitting, to produce these mineral identifications. Detection and quantitative analysis of these absorptions provide a much improved basis for remotely determining and mapping surface mineralogy quantitatively from the ground or using airborne or spacecraft platforms.