Statistical weak lensing by large-scale structure { cosmic shear { is a promising cosmological tool, which has motivated the design of several large upcoming astronomical surveys. This Thesis presents a measurement of cosmic shear using coadded Sloan Digital Sky Survey (SDSS) imaging in 168 square degrees of the equatorial region, with r < 23:5 and i < 22:5, a source number density of 2.2 per arcmin² and median redshift of z_med = 0.52. These coadds were generated using a new rounding kernel method that was intended to minimize systematic errors in the lensing measurement due to coherent PSF anisotropies that are otherwise prevalent in the SDSS imaging data. Measurements of cosmic shear out to angular separations of 2 degrees are presented, along with systematics tests of the catalog generation and shear measurement steps that demonstrate that these results are dominated by statistical rather than systematic errors. Assuming a cosmological model corresponding to WMAP7

(Komatsu et al., 2011) and allowing only the amplitude of matter fluctuations &sigma₈ to vary, the best-t value of the amplitude of matter fluctuations is &sigma₈=0.636^+0.109_-0.154 (1&sigma); without systematic errors this would be &sigma₈=0.636^+0.099_-0.137 (1&sigma). Assuming a flat &LambdaCDM model, the combined constraints with WMAP7 are &sigma₈=0.784super>+0.028_-0.026 (1&sigma). The 2&sigma error range is 14 percent smaller than WMAP7 alone. Aside from the intrinsic value of such cosmological constraints from the growth of structure, some important lessons are identied for upcoming surveys that may face similar issues when combining multi-epoch data to measure cosmic shear.

Motivated by the challenges faced in the cosmic shear measurement, two new lensing probes are suggested for increasing the available weak lensing signal. Both use galaxy scaling relations to control for scatter in lensing observables.

The first employs a version of the well-known fundamental plane relation for early type galaxies. This modified "photometric fundamental plane" replaces velocity dispersions with photometric galaxy properties, thus obviating the need for spectroscopic data. We present the first detection of magnication using this method by applying it to photometric catalogs from the Sloan Digital Sky Survey. This analysis shows that the derived magnication signal

is comparable to that available from conventional methods using gravitational shear. We suppress the dominant sources of systematic error and discuss modest improvements that may allow this method to equal or even surpass the signal-to-noise achievable with shear. Moreover, some of the dominant sources of systematic error are substantially different from those of shear-based techniques.

The second outlines an idea for using the optical Tully-Fisher relation to dramatically improve the signal-to-noise and systematic error control for shear measurements. The expected

error properties and potential advantages of such a measurement are proposed, and a pilot study is suggested in order to test the viability of Tully-Fisher weak lensing in the context of the forthcoming generation of large spectroscopic surveys.