Libraries of stellar spectra are fundamental tools for the study of stellar populations, and both empirical and synthetic libraries have been used for this purpose. In this paper, a new library of high resolution synthetic spectra is presented, ranging from the near-ultraviolet (300 nm) to the near-infrared (1.8 mu m). The library spans all the stellar types that are relevant to the integrated light of old and intermediate-age stellar populations in the involved spectral region (spectral types F through M and all luminosity classes). The grid was computed for metallicities ranging from Fe/H = -2.5 to +0.5, including both solar and alpha -enhanced ( alpha /Fe = 0.4) chemical compositions. The synthetic spectra are a good match to observations of stars throughout the stellar parameter space encompassed by the library and over the whole spectral region covered by the computations.