  We describe the NIRSpec component of the JWST Deep Extragalactic Survey
(JADES), and provide deep spectroscopy of 253 sources targeted with the NIRSpec
micro-shutter assembly in the Hubble Ultra Deep Field and surrounding
GOODS-South. The multi-object spectra presented here are the deepest so far
obtained with JWST, amounting to up to 28 hours in the low-dispersion ($R\sim
30-300$) prism, and up to 7 hours in each of the three medium-resolution
$R\approx 1000$ gratings and one high-dispersion grating, G395H
($R\approx2700$). Our low-dispersion and medium-dispersion spectra cover the
wavelength range $0.6-5.3\mu$m. We describe the selection of the spectroscopic
targets, the strategy for the allocation of targets to micro-shutters, and the
design of the observations. We present the public release of the reduced 2D and
1D spectra, and a description of the reduction and calibration process. We
measure spectroscopic redshifts for 178 of the objects targeted extending up to
$z=13.2$. We present a catalog of all emission lines detected at $S/N>5$, and
our redshift determinations for the targets. Combined with the first JADES
NIRCam data release, these public JADES spectroscopic and imaging datasets
provide a new foundation for discoveries of the infrared universe by the
worldwide scientific community.
