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We obtained Hubble GHRS phase-resolved spectroscopic observations of the dwarf nova RX Andromedae at three times in its outburst cycle: (1) near the end of an extraordinarily deep and long dwarf nova quiescence, 3 months after the last previous outburst; (2) during the rise to outburst; and (3) near the end of a decline from outburst. The spectral wavelength range covered was 1149Angstroms to 1435Angstroms. All of the spectra are dominated by absorption lines with weak to moderately strong emission wings due to the continued presence of disk material. Uncertainities in line velocities preclude a K1 determination or mass information. Our best fitting model yielded Twd/1000 = 34.0 ± 0.1K, log g = 8.0 ± 0.1, and Vrot = 600 +200/-100 km/s. The Teff value is very similar to the Teff of the white dwarf in U Gem, but the rotational velocity appears to be higher than U Gem's value. We report approximate subsolar chemical abundances of Carbon and Silicon for RX And, with C being 0.05 x solar and Si = 0.1 x solar while other elements are at essentially their solar values. However, accurate abundances are complicated by line emission and we cannot exclude that the abundances of all species are essentially at the solar values. We see no evidence of thermonuclear-processed abundance ratios. If the white dwarf mass is 0.8 M (Ritter 1999), then the corresponding white dwarf cooling age, 4 x 106 years, is a lower limit to the age of this CV. If the peculiar line features seen in the spectrum on the late decline from outburst are inverse P Cygni in nature, then infall velocities of ∼2000km/s are indicated during the decline from outburst. We compare the surface properties of the RX And white dwarf with the properties of other CV degenerates studied to date with HST, HUT, and IUE.