The release of the MUSE gAlaxy Groups In COSMOS (MAGIC) survey (Programmes 094.A-0247, 095.A-0118, 096.A-0596, 097.A-0254, 098.A-0017, 099.A-0246, 0100.A-0607, 0101.A-0282, 0102.A-0327, 0103.A-0563, PI T. Contini) is composed of 18 datacubes, observed with exposure times from 1 to 10 hours, with a median of 4.3 hours, using the wide-field mode, with a spectral sampling of 1.25 Angstroms and a spatial sampling of 0.2 arcsecond. The datacubes cover the wavelength range between 4700 and 9350 Angstroms and have an image quality better than 0.7" FWHM owing to good observing conditions and/or to the use of adaptive optics. The median 3-sigma point-source flux limit of an unresolved emission line reaches 3.6x10^-19 erg s^-1 cm^-2 and the median point source magnitude limit is about 28.5 at 5-sigma in white-light images. The MAGIC survey datacubes target 15 known massive groups and clusters at intermediate redshift (0.3 < z < 0.8), 14 of which being located in the COSMOS field and one in the VVDS field. This dataset is incredibly rich and contains more than one thousand of objects, from stars to high redshift galaxies, as well as extended nebulae.