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 is to assemble a large sample of X-ray 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 12,247 optically confirmed galaxy groups and clusters detected in the 0.2-2.3keV as extended X-ray sources in a 13116 deg^2^ region in the western Galactic half 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 5x10^12^M_{sun}_ to 2x10^15^M_{sun}_. We construct a sample for cosmology with a higher purity level (~95%) than the primary sample, comprising 5,259 securely detected and confirmed clusters in the 12791 deg^2^ common footprint of eRASS1 and 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 YX. These are determined within two apertures, 300kpc, and the overdensity radius R500, 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 through the selection function. The first eROSITA All-Sky Survey provides an unprecedented sample of galaxy groups and clusters selected in the X-ray band. The eRASS1 cluster catalog demonstrates the excellent performance of eROSITA for extended source detection, consistent with the pre-launch expectations for the final all-sky survey, eRASS:8.