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We present the second data release of the MUSE Hubble UDF surveys, which includes the deepest spectroscopic survey ever performed. The MUSE data, with their 3D content, amazing depth, wide spectral range, and excellent spatial and medium spectral resolution, are rich in information. This update of the first release incorporates a new 141-hour adaptive-optics-assisted MXDF field (1' diameter FoV) in addition to the reprocessed 10-hour mosaic (3'x3') and the single 31-hour deep field (1'x1'). We have securely identified and measured the redshift of 2221 sources, an increase of 41% compared to the first release. With the exception of 8 stars, the collected sample consists of 25 nearby galaxies (z < 0.25), 677 OII emitters (z=0.25-1.5), 201 galaxies in the MUSE redshift desert range (z=1.5-2.8), and 1308 LAEs (z=2.8-6.7). This represents an order of magnitude more redshifts than the collection of all spectroscopic redshifts obtained before MUSE in the Hubble UDF area (2221 vs 292). At z > 3, the difference is even more striking, with a factor of 65 increase (1308 vs 20). We compared the measured redshifts against three published photometric redshift catalogs and find the photo-z accuracy to be lower than the constraints provided by photo-z fitting codes. 80% of the galaxies have an HST counterpart. They are on average faint, with a median magnitude of 25.7 and 28.7 for the OII and Ly-alpha emitters, respectively. SED fits show that these galaxies tend to be low-mass star-forming galaxies, with a median stellar mass of 6.2 10**8 M and a median SFR of 0.4 M/yr. 20% of our catalog, or 424 galaxies, have no HST counterpart. The vast majority of these new sources are high EQW z>2.8 LAEs that are detected by MUSE thanks to their bright and asymmetric broad Ly-alpha line. We release advanced data products, specific software, and a web interface to select and download data sets.