The HST Treasury Program Advanced Spectral Library Project: Cool Stars was designed to collect representative, high quality ultraviolet spectra of eight evolved F-M type cool stars. The Space Telescope Imaging Spectrograph (STIS) echelle spectra of these objects enable investigations of a broad range of topics including stellar and interstellar astrophysics. This paper provides a guide to the spectra of the two evolved M-stars, the M2Iab supergiant Alpha Ori and the M3.4 giant Gamma Cru, with comparisons to the prototypical K1.5 giant Alpha Boo. It includes identifications of the significant atomic and molecular emission and absorption features and discusses the character of the photospheric and chromospheric continua and line spectra. The fluorescent processes responsible for a large portion of the emission line spectrum, the characteristics of the stellar winds, and the available diagnostics for hot and cool plasmas are also summarized. This analysis will facilitate the future study of the spectra, outer atmospheres, and winds, not only of these objects, but for numerous other cool, low-gravity stars for years to come.
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