  We present the extended GALEX Arecibo SDSS Survey (xGASS), a gas
fraction-limited census of the atomic (HI) gas content of 1179 galaxies
selected only by stellar mass ($M_\star =10^{9}-10^{11.5} M_\odot$) and
redshift ($0.01<z<0.05$). This includes new Arecibo observations of 208
galaxies, for which we release catalogs and HI spectra. In addition to
extending the GASS HI scaling relations by one decade in stellar mass, we
quantify total (atomic+molecular) cold gas fractions and molecular-to-atomic
gas mass ratios, $R_{mol}$, for the subset of 477 galaxies observed with the
IRAM 30 m telescope. We find that atomic gas fractions keep increasing with
decreasing stellar mass, with no sign of a plateau down to $\log
M_\star/M_\odot = 9$. Total gas reservoirs remain HI-dominated across our full
stellar mass range, hence total gas fraction scaling relations closely resemble
atomic ones, but with a scatter that strongly correlates with $R_{mol}$,
especially at fixed specific star formation rate. On average, $R_{mol}$ weakly
increases with stellar mass and stellar surface density $\mu_\star$, but
individual values vary by almost two orders of magnitude at fixed $M_\star$ or
$\mu_\star$. We show that, for galaxies on the star-forming sequence,
variations of $R_{mol}$ are mostly driven by changes of the HI reservoirs, with
a clear dependence on $\mu_\star$. Establishing if galaxy mass or structure
plays the most important role in regulating the cold gas content of galaxies
requires an accurate separation of bulge and disk components for the study of
gas scaling relations.
