We present the second campaign of the ESO/GOODS program of spectroscopy of faint galaxies in the GOODS-South field. Objects were selected as candidates for VLT/FORS2 observations primarily based on the expectation that the detection and measurement of their spectral features would benefit from the high throughput and spectral resolution of FORS2. The reliability of the redshift estimates is assessed using the redshift-magnitude and color-redshift diagrams and comparing the results with public data. 807 spectra of 652 individua targets have been obtained in service mode with the FORS2 spectrograph at the ESO/VLT, providing 501 redshift determinations. The typical redshift uncertainty is estimated to be sigma_z ~ 0.001. Galaxies have been selected adopting three different color criteria and using the photometric redshifts.The resulting redshift distribution typically spans two redshift domains: from z=0.5 to 2 and z=3.5 to 6.2. In particular, 94 B435-,V606-,i775 dropout Lyman break galaxies have been observed, yielding redshifts for 65 objects in the interval 3.4<z<6.2. Three sources have been serendipitously discovered in the redshift interval 4.8<z<5.5. Together with the previous release, 930 sources have now been observed and 724 redshift determinations have been carried out. The reduced spectra and the derived redshifts are released to the community through the ESO web page http://www.eso.org/science/goods/. Large scale structures are clearly detected at z=0.666, 0.734, 1.096, 1.221, 1.300, and 1.614. A sample of 34 sources with tilted [OII]3727 emission has been identified, 32 of them in the redshift range 0.9<z<1.5.
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