We present the MUSE-Wide survey, a blind, 3D spectroscopic survey in the CANDELS/GOODS-S and CANDELS/COSMOS regions. Each MUSE-Wide pointing has a depth of 1 hour and hence targets more extreme and more luminous objects over 10 times the area of the MUSE-Deep fields (Bacon et al. 2017). The legacy value of MUSE-Wide lies in providing spectroscopy of everything without photometric pre-selection. We describe the data reduction, post-processing and PSF characterization of the first 44 CANDELS/GOODS-S MUSE-Wide pointings released with this publication. Using a 3D matched filtering approach we detected 1,602 emission line sources, including 479 Lyman-$alpha$ (Lya) emitting galaxies with redshifts $2.9 lesssim z lesssim 6.3$. We cross-match the emission line sources to existing photometric catalogs, finding almost complete agreement in redshifts and stellar masses for our low redshift (z < 1.5) emitters. At high redshift, we only find ~55% matches to photometric catalogs. We encounter a higher outlier rate and a systematic offset of $Delta$z$simeq$0.2 when comparing our MUSE redshifts with photometric redshifts. Cross-matching the emission line sources with X-ray catalogs from the Chandra Deep Field South, we find 127 matches, including 10 objects with no prior spectroscopic identification. Stacking X-ray images centered on our Lya emitters yielded no signal; the Lya population is not dominated by even low luminosity AGN. A total of 9,205 photometrically selected objects from the CANDELS survey lie in the MUSE-Wide footprint, which we provide optimally extracted 1D spectra of. We are able to determine the spectroscopic redshift of 98% of 772 photometrically selected galaxies brighter than 24th F775W magnitude. All the data in the first data release - datacubes, catalogs, extracted spectra, maps - are available on the website https://musewide.aip.de. [abridged]
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