  We present the first analysis of the Euclid Early Release Observations (ERO)
program that targets fields around two lensing clusters, Abell 2390 and Abell
2764. We use VIS and NISP imaging to produce photometric catalogs for a total
of $\sim 500\,000$ objects. The imaging data reach a $5\,\sigma$ typical depth
in the range 25.1-25.4 AB in the NISP bands, and 27.1-27.3 AB in the VIS band.
Using the Lyman-break method in combination with photometric redshifts, we
identify $30$ Lyman-break galaxy (LBG) candidates at $z>6$ and 139 extremely
red sources (ERSs), most likely at lower redshift. The deeper VIS imaging
compared to NISP means we can routinely identify high-redshift Lyman breaks of
the order of $3$ magnitudes, which reduces contamination by brown dwarf stars
and low-redshift galaxies. Spectroscopic follow-up campaigns of such bright
sources will help constrain both the bright end of the ultraviolet galaxy
luminosity function and the quasar luminosity function at $z>6$, and constrain
the physical nature of these objects. Additionally, we have performed a
combined strong lensing and weak lensing analysis of A2390, and demonstrate how
Euclid will contribute to better constraining the virial mass of galaxy
clusters. From these data, we also identify optical and near-infrared
counterparts of known $z>0.6$ clusters, which exhibit strong lensing features,
establishing the ability of Euclid to characterize high-redshift clusters.
Finally, we provide a glimpse of Euclid's ability to map the intracluster light
out to larger radii than current facilities, enabling a better understanding of
the cluster assembly history and mapping of the dark matter distribution. This
initial dataset illustrates the diverse spectrum of legacy science that will be
enabled by the Euclid survey.
