The 'Cordoba Durchmusterung' (CD) is a visual survey of southern stars in the declination zones -22 to -89 deg, carried out as an extension to the 'Bonner Durchmusterung' (BD) catalogs of Argelander and Schoenfeld. This volume covers the declination range -31 deg through -39 deg. The survey was performed using techniques similar to those used for the BD; i.e., the stars were cataloged by allowing the telescope to drift along the mean declination of each zone and recording the positions and magnitudes of stars crossing the transit line of the field. The goal of the survey was to obtain a position and estimated visual magnitude for every star down to 10.0 magnitude inclusive, but the faint limit was confirmed from comparisons with other catalogs, to be somewhat below 10. The positions are given to 0.1 s in right ascension and 0.1 min in declination for the equinox 1875. The positional uncertainties quoted in the original publications are plus or minus 0.42 s and plus or minus 0.23 min for zones -22 deg to -32 deg. A list of all corrections made to the original data as a result of published corrigenda is presented. No other corrections or changes were incorporated into the original data, e.g., from more modern positions and magnitudes or comparison with the 'Cape Photographic Durchmusterung'.