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We introduce the MUSE gAlaxy Groups in COSMOS (MAGIC) survey, which was builtto study the impact of environment on galaxy evolution over the last 8 Gyr. Itconsists of 17 MUSE fields targeting 14 massive structures at intermediateredshift ($0.3<z<0.8$) in the COSMOS area. We securely measured the redshiftsfor 1419 sources and identified 76 galaxy pairs and 67 groups of at least 3members using a friends-of-friends algorithm. The environment of galaxies isquantified from group properties, as well as from global and local densityestimators. The MAGIC survey has increased the number of objects with a securespectroscopic redshift over its footprint by a factor of about 5. Most of thenew redshifts have apparent magnitudes in the $z^{++}$ band$z_{app}^{++}>21.5$. The spectroscopic redshift completeness is high: in theredshift range of [OII] emitters ($0.25 \le z < 1.5$), where most of the groupsare found, it globally reaches a maximum of 80% down to $z_{app}^{++}=25.9$,and locally decreases from $\sim 100$% to $\sim50$% in magnitude bins from$z_{app}^{++}=23-24$ to $z_{app}^{++}=25.5$. We find that the fraction ofquiescent galaxies increases with local density and with the time spent ingroups. A morphological dichotomy is also found between bulge-dominatedquiescent and disk-dominated star-forming galaxies. As environment gets denser,the peak of the stellar mass distribution shifts towards $M_*>10^{10}~M_\odot$,and the fraction of galaxies with $M_*<10^9~M_\odot$ decreases significantly,even for star-forming galaxies. We also highlight peculiar features such asclose groups, extended nebulae, and a gravitational arc. Our results suggestthat galaxies are preprocessed in groups of increasing mass before enteringrich groups and clusters. We publicly release two catalogs containing theproperties of galaxies and groups, respectively.

MAGIC: Muse gAlaxy Groups In Cosmos -- A survey to probe the impact of environment on galaxy evolution over the last 8 Gyr