(abridged) We present deep spectroscopy of a large sample of low-metallicity emission-line galaxies. The main goal of this study is to derive element abundances in these low-metallicity galaxies. We analyze 121 VLT spectra of HII regions in 46 low-metallicity emission-line galaxies. 83 of these spectra are archival VLT/FORS1+UVES spectra of HII regions in 31 low-metallicity emission-line galaxies that are studied for the first time with standard direct methods to determine the electron temperatures, the electron number densities, and the chemical abundances. The oxygen abundance of the sample lies in the range 12 + log O/H = 7.2-8.4. The Ne/O ratio increases with increasing oxygen abundance. The Fe/O ratio decreases from roughly solar at the lowest metallicities to about one tenth of solar, indicating that the degree of depletion of iron into dust grains depends on metallicity. The N/O ratio in extremely low-metallicity galaxies with 12+logO/H<7.5 shows a slight increase with decreasing oxygen abundance. We present the first empirical relation between the electron temperature derived from [SIII]6312/9069 or [NII]5755/6583 and the one derived from [OIII]4363/(4959+5007) in low-metallicity galaxies. In a number of objects, the abundances of C^++ and O^++ could be derived from recombination lines. Our study confirms the discrepancy between abundances found from recombination lines (RLs) and collisionally excited lines (CELs) and that C/O increases with O/H.
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