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The eROSITA Final Equatorial-Depth Survey has been carried out during the PVphase of the SRG/eROSITA telescope and completed in November 2019. This surveyis designed to provide the first eROSITA-selected sample of galaxy clusters andgroups and to test the predictions for the all-sky survey in the context ofcosmological studies with clusters. In the 140 deg$^2$ area covered by eFEDS,542 candidate clusters and groups are detected as extended X-ray sources, downto a flux of $\sim10^{-14} $erg/s/cm$^2$ in the soft band (0.5-2 keV) within1'. In this work, we provide the catalog of candidate galaxy clusters andgroups in eFEDS. We perform imaging and spectral analysis on the eFEDS clusterswith eROSITA X-ray data, and study the properties of the sample. The clustersare distributed in the redshift range [0.01, 1.3], with the median redshift at0.35. We obtain the ICM temperature measurement with $>2\sigma$ c.l. for$\sim$1/5 (102/542) of the sample. The average temperature of these clusters is$\sim$2 keV. Radial profiles of flux, luminosity, electron density, and gasmass are measured from the precise modeling of the imaging data. The selectionfunction, the purity and completeness of the catalog are examined and discussedin detail. The contamination fraction is $\sim1/5$ in this sample, dominated bymisidentified point sources. The X-ray Luminosity Function of the clustersagrees well with the results obtained from other recent X-ray surveys. We alsofind 19 supercluster candidates in eFEDS, most of which are located atredshifts between 0.1 and 0.5. The eFEDS cluster and group catalog provides abenchmark proof-of-concept for the eROSITA All-Sky Survey extended sourcedetection and characterization. We confirm the excellent performance of eROSITAfor cluster science and expect no significant deviations from our pre-launchexpectations for the final All-Sky Survey.

The eROSITA Final Equatorial-Depth Survey (eFEDS): Catalog of galaxy clusters and groups