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We conducted a deep spectroscopic survey, named SSA22-HIT, in the SSA22 field with the DEep Imaging MultiObject Spectrograph (DEIMOS) on the Keck telescope, designed to tomographically map high- z H i gas through analysis of Ly α absorption in background galaxies’ spectra. In total, 198 galaxies were spectroscopically confirmed at 2.5 < z < 6 with a few low- z exceptions in the 26 × 15 arcmin ^2 area, of which 148 were newly determined in this study. Our redshift measurements were merged with previously confirmed redshifts available in the 34 × 27 arcmin ^2 area of the SSA22 field. This compiled catalog containing 730 galaxies of various types at z > 2 is useful for various applications, and it is made publicly available. Our SSA22-HIT survey has increased by approximately twice the number of spectroscopic redshifts of sources at z > 3.2 in the observed field. From a comparison with publicly available redshift catalogs, we show that our compiled redshift catalog in the SSA22 field is comparable to those among major extragalactic survey fields in terms of a combination of wide area and high surface number density of objects at z > 2. About 40% of the spectroscopically confirmed objects in SSA22-HIT show reasonable quality of spectra in the wavelengths shorter than Ly α when a sufficient amount of smoothing is adopted. Our data set enables us to make the H i tomographic map at z ≳ 3, which we present in a parallel study.