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A new three-angle energy-dispersive (ED) diffractometer has been successfully commissioned on station 16.4 SRS, Daresbury, England. The diffractometer facilitates the simultaneous collection of three spectra at three Bragg scattering angles. This enables the sampling of a far greater range of reciprocal space as compared to conventional single-angle diffractometers. Additionally the arrangement allows changes in sample density to be monitored. A protocol has been developed to align the diffractometer such that the origins of the diffracting volume are coincident on the diffractometer axis. Spectra obtained from the diffractometer were improved by the construction and placement of shielding. Experimental determination of components of the resolution function show that the resolution is close to the instrumental limit. The flux distribution of station 16.4 was determined experimentally. A novel whole pattern method has been developed for the quantitative analysis of synchrotron ED diffraction data. The method, which accounts for the differential absorption across the ED spectrum, was developed using spectra collected from a set of test binary phase mixtures and pure phases. Parameters relating to the proposed models were determined using linear and non-linear least-squares methods. Although the final model is the most physically complete it does not take account of certain non-diffraction derived events which appear as counts within the test spectra. A novel application of synchrotron ED diffraction, energy-dispersive diffraction tomography (EDD-T), is described. The method facilitates the non-destructive examination of the interior of crystalline and semi-crystalline objects. The resolution and limitations of this technique have been demonstrated using test objects. The method has been used to map the phase distributions of a variety of materials in a range of different samples. Quantitative EDD-T was used to determine the invasion of calcite into simulated oil-reservoir rocks.