This thesis describes an investigation into weak gravitational lensing, a unique and powerful astronomical tool for the study of dark matter on large scales. Lensing distorts background images, inducing correlations in the observed ellipticities of galaxies, and these correlations can be used to estimate many characteristics of the Universe. Key to all weak lensing studies is a reliable and unbiased method to detect weak lensing distortions from observed galaxy images that are contaminated by Earth and telescope-based shearing and smearing distortions. A new galaxy model-fitting technique is presented that has been developed in order to satisfy this requirement, which will also permit future signal-to-noise optimised measurements of weak lensing shear. Model-fitting provides a good alternative to the standard scite{KSB} method (KSB), and comparisons between the two techniques are drawn from an analysis of deep {it R} band imaging from the COMBO-17 survey, revealing strong evidence for the presence of bias in KSB galaxy shape measurement. With the galaxy model-fitting technique, an investigation into the effectiveness of the Oxford Dartmouth Thirty degree survey (ODT) for gravitational lensing studies is presented, resulting in the detection of weak gravitational lensing by large scale structure, or `cosmic shear', in 0.7 square degrees of the best seeing ODT images. One concern for all cosmic shear studies is that the weak lensing signal, manifest in the weakly correlated ellipticities of distant galaxies, is contaminated by the intrinsic alignment of close galaxy pairs, potentially induced during galaxy formation by physical interactions such as tidal forces. This contamination is investigated theoretically, through numerical simulations, and observationally, with an analysis of the COMBO-17 survey and the study of published results from the Red-sequence Cluster survey and the VIRMOS-DESCART survey, concluding that the intrinsic alignment effect is at the lower end of the range of theoretical predictions. The impact of intrinsic galaxy alignments on cosmological parameter estimation is investigated, with an analysis of the weak lensing results from the COMBO-17 survey. When marginalising over the observationally constrained intrinsic alignment signal, the amplitude of the matter power spectrum sigma_8 is reduced by ~0.03 to sigma_8(Omega_m / 0.27)^{0.6} = 0.71 pm 0.11, where Omega_m is the matter density parameter. With distance information from either spectroscopy or photometric redshifts, the down-weighting of nearby galaxy pairs in weak lensing analysis can be optimised to virtually eliminate the systematic errors in the shear signal arising from intrinsic galaxy alignments, leaving a much smaller, largely statistical error. This method is applied to the photometric redshift sample of the COMBO-17 survey. Weak lensing measurements from the forthcoming SuperNova/Acceleration Probe weak lensing survey (SNAP), and the Canada-France-Hawaii Telescope Legacy survey, are expected to be contaminated on scales >1 arcminute by intrinsic alignments at the level of ~ 1% and ~2% respectively. Division of the SNAP survey for lensing tomography significantly increases the contamination in the lowest redshift bin to ~7% and possibly higher. Removal of the intrinsic alignment effect by the downweighting of nearby galaxy pairs will therefore be vital for the lensing tomography studies of SNAP.