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This thesis centers on the use of spectral modeling techniques on data from the Sloan Digital Sky Survey (SDSS) to gain new insights into current questions in galaxy evolution. The SDSS provides a large, uniform, high quality data set which can be exploited in a number of ways. One avenue pursued here is to use the large sample size to measure precisely the mean properties of galaxies of increasingly narrow parameter ranges. The other route taken is to look for rare objects which open up for exploration new areas in galaxy parameter space. The crux of this thesis is revisiting the classical Kennicutt method for inferring the stellar initial mass function (IMF) from the integrated light properties of galaxies. A large data set ({approx} 10{sup 5} galaxies) from the SDSS DR4 is combined with more in-depth modeling and quantitative statistical analysis to search for systematic IMF variations as a function of galaxy luminosity. Galaxy H{alpha} equivalent widths are compared to a broadband color index to constrain the IMF. It is found that for the sample as a whole the best fitting IMF power law slope above 0.5 M{sub {circle_dot}} is {Lambda} = 1.5 {+-} 0.1 with the error dominated by systematics. Galaxies brighter than around M{sub r,0.1} = -20 (including galaxies like the Milky Way which has M{sub r,0.1} {approx} -21) are well fit by a universal {Lambda} {approx} 1.4 IMF, similar to the classical Salpeter slope, and smooth, exponential star formation histories (SFH). Fainter galaxies prefer steeper IMFs and the quality of the fits reveal that for these galaxies a universal IMF with smooth SFHs is actually a poor assumption. Related projects are also pursued. A targeted photometric search is conducted for strongly lensed Lyman break galaxies (LBG) similar to MS1512-cB58. The evolution of the photometric selection technique is described as are the results of spectroscopic follow-up of the best targets. The serendipitous discovery of two interesting blue compact dwarf galaxies is reported. These galaxies were identified by their extremely weak (&lt; 150) [N {pi}] {lambda}6584 to H{alpha} emission line ratios. Abundance analysis from emission line fluxes reveals that these galaxies have gas phase oxygen abundances 12 + log(O/H) {approx} 7.7 to 7.9, not remarkably low, and near infrared imaging detects an old stellar population. However, the measured nitrogen to oxygen ratios log(N/O) &lt; 1.7 are anomalously low for blue compact dwarf galaxies. These objects may be useful for understanding the chemical evolution of nitrogen

Galaxy Evolution Insights from Spectral Modeling of Large Data Sets from the Sloan Digital Sky Survey