  Clusters of galaxies can be used as powerful probes to study astrophysical
processes on large scales, test theories of the growth of structure, and
constrain cosmological models. The driving science goal of the SRG/eROSITA
All-Sky Survey (eRASS) is to assemble a large sample of X-ray-selected clusters
with a well-defined selection function to determine the evolution of the mass
function and, hence, the cosmological parameters. We present here a catalog of
12247 optically confirmed galaxy groups and clusters detected in the 0.2-2.3
keV as extended X-ray sources in a 13,116deg$^2$ region in the western Galactic
hemisphere of the sky, which eROSITA surveyed in its first six months of
operation. The clusters in the sample span the redshift range $0.003<z<1.32$.
The majority (68%) of these clusters, 8361 sources, represent new discoveries
without known counterparts in the literature. The mass range of the sample
covers three orders of magnitude from $5\times10^{12}M_{\rm sun}$ to
$2\times10^{15}M_{\rm sun}$. We construct a sample for cosmology with a higher
purity level (~95%) than the primary sample, comprising 5259 securely detected
and confirmed clusters in the 12791deg$^{2}$ common footprint with the DESI
Legacy Survey DR10. We characterize the X-ray properties of each cluster,
including their flux, luminosity and temperature, the total mass, gas mass, gas
mass fraction, and mass proxy $Y_{X}$. These are determined within two
apertures, 300 kpc, and the overdensity radius $R_{500}$, and are calculated by
applying a forward modeling approach with a rigorous X-ray background
treatment, K-factor, and the Galactic absorption corrections. Population
studies utilizing LogN-LogS, the number of clusters detected above a given flux
limit, and the luminosity function show overall agreement with the previous
X-ray surveys after accounting for the survey completeness and purity
(ABRIDGED)
