In this thesis we begin to unify two pictures of the high redshift universe: absorption line systems such as damped Lyman alpha systems (DLAs) that provide the fuel for star formation, and compact star forming regions such as Lyman break galaxies (LBGs) which form the majority of stars. Wolfe & Chen (2006) find that the in situ star formation in DLAs is less than 5% of what is expected from the Kennicutt-Schmidt (KS) relation, but they do not constrain DLAs associated with bright star-forming regions such as LBGs. In this work we search for spatially-extended star formation in the outskirts of LBGs at z3̃. To this end, we create a sample of z3̃ LBGs in the Hubble Ultra Deep Field (UDF) by using photometric redshifts enabled by the introduction of an extremely deep u-band image. By stacking these galaxies, we find spatially extended low surface brightness emission around LBGs in the V-band image of the UDF, corresponding to the z3̃ rest-frame far- ultraviolet light, which is a sensitive measure of star formation rates (SFRs). We connect this emission around LBGs to the expected emission from DLAs, and the results suggest that the SFR efficiency in such gas at z3̃ is between factors of 10 and 50 lower than predictions based on the KS relation. This decreased efficiency is likely due to the lower metallicity of DLA gas. In addition, we measure the metallicity evolution of DLAs out to z5̃, and find a continued decrease of metallicity with increasing redshift and a metallicity "floor'' around one thousandth of the solar value. We also compare the metallicity distribution and chemistry of DLAs and halo stars, and find that they are not inconsistent. Lastly, we study the photometric variability of stars in the Galactic center in order to further our understanding of the massive young stars forming in the presence of a super massive black hole. All together, these results improve our understanding of star formation and provide constraints for models and simulations of galaxy formation and evolution that will yield a more complete understanding of star formation across cosmic time