The Damped and sub-Damped Lyman- \alpha ( DLA and sub-DLA ) systems seen in the spectra of QSOs offer a unique way to study the interstellar medium of high redshift galaxies . In this paper we report on new abundance determinations in a sample of 10 new systems , nine of the lesser studied sub-DLAs and one DLA , along the line of sight to seven QSOs from spectra taken with the MIKE spectrograph . Lines of Mg I , Mg II , Al II , Al III , Ca II , Mn II , Fe II , and Zn II were detected . Here , we give the column densities and equivalent widths of the observed absorption lines , as well as the abundances determined for these systems . Zn , a relatively undepleted element in the local interstellar medium ( ISM ) is detected in one system with a high metallicity of [ Zn/H ] =+0.27 \pm 0.18 . In one other system , a high abundance based on the more depleted element Fe is seen with [ Fe/H ] = -0.37 \pm 0.13 , although Zn is not detected . The N _ { H I } -weighted mean metallicity of these sub-DLA systems based on Fe is \langle [ Fe/H ] \rangle = -0.76 \pm 0.11 , nearly \sim 0.7 dex higher ( a factor of 5 ) than what is seen in DLAs in this redshift range . The relative abundance of [ Mn/Fe ] is also investigated . A clear trend is visible for these systems as well as systems from the literature , with [ Mn/Fe ] increasing with increasing metallicity in good agreement with with Milky Way stellar abundances .