We present a series of early UVES/VLT high resolution spectra of the afterglow of GRB 030329 at redshift z = 0.16867 \pm 0.00001 . In contrast to other spectra from this burst , both emission and absorption lines were detected . None of them showed any temporal evolution . From the emission lines , we determine the properties of the host galaxy which has a star formation rate ( SFR ) of 0.198 M _ { \odot } yr ^ { -1 } and a low metallicity of 1/7 Z _ { \odot } . Given the low total stellar host mass M _ { \star } =10 ^ { 7.75 \pm 0.15 } M _ { \odot } and an absolute luminosity m _ { \mathrm { V } } =–16.37 , we derive specific SFRs ( SSFR ) of log SFR/M = –8.5 yr ^ { -1 } and SFR/L = 14.1 M _ { \odot } yr ^ { -1 } L _ { * } ^ { -1 } . This fits well into the picture of GRB hosts as being low mass , low metallicity , actively star forming galaxies . The Mg ii and Mg i absorption lines from the host show multiple narrow ( Doppler width b=5-10 km/s ) components spanning a range of v \sim 260 km/s , mainly blueshifted compared to the redshift from the emission lines . These components are likely probing outflowing material of the host galaxy , which could arise from former galactic superwinds , driven by supernovae from star forming regions . Similar features have been observed in QSO spectra . The outflowing material is mainly neutral with high column densities of log N ( Mg ii ) = { 14.0 \pm 0.1 } cm ^ { -2 } and log N ( Mg i ) = { 12.3 \pm 0.1 } cm ^ { -2 } .