In the high-temperature superconductor YBa2Cu307_0 (YBCO) the superconducting properties are a function of oxygen stoichiometry. In the case where 8=0 the material is a superconductor, and when O=l an antiferromagnetic insulator. In the production of bulk superconductors the oxygen anneal is therefore important in determining the properties of the sample. Studies on critical currents in bulk materials and single cystals have shown that the currents in the bulk materials are a factor of 10 less than for the single crystals. This discrepancy can be associated with a change in oxygen stoichiometry at the boundary or the presence of impurity phases. Previous studies of oxygen stoichiometry have been on the micron scale-or greater, which do not allow the fluctuations near boundaries to be observed. By using a Scanning Transmission Electron Microscope (STEM) to study the fluctuations in stoichiometry, the sub-nanometre probe (-0.5nm) allows spatial resolution on the nanometre scale. Coupling the nanometre spatial resolution with electron energy loss spectroscopy (EELS), which allows accurate observation of light elements such as oxygen, gives the opportunity to observe fluctuations in stoichiometry to -2%. The oxygen Kabsorption edge has previously been shown to have a pre-edge feature which shows intensity variations proportional to oxygen stoichiometry. A method has been determined whereby the variation in pre-edge intensity can be used to give an estimate of absolute oxygen stoichiometry. This quantification of oxygen stoichiometry has been calibrated in reference to a series of compounds prepared with different starting stoichiometries. The calibration of the pre-edge feature can then be used to quantify fluctuations at boundaries in both crushed and ion-beam thinned materials. In the case of the ion-beam thinned materials the problems associated with ion-beam damage during preparation are described with reference to the interpretation of the results. The crystal structure of YBCO is orthorhombic and as such the energy loss spectrum obtained in STEM will show an orientation dependence. The description of Ritchie (1957) for the energy loss function for an isotropic medium is adapted to account for the anisotropic structure of high-temperature superconductors. From the equations derived it is possible to decompose the angular integrated core loss spectra obtained in the STEM into two (layered materials) or three (orthorhombic materials) orthogonal components. The components can be used to simulate the spectra that can be expected from all possible orientations and collection conditions. The equations derived are verified by the decomposition of the angular integrated carbon K-edge spectrum from graphite into two orthogonal components. The components of the oxygen K-edge from YBa2Cu307_0 are decomposed from the experimental spectra and used to investigate the band structure of the material. By obtaining spectra from different orientations and spectra with different collection conditions, the dipole approximation can be investigated for commonly used apertures in the STEM. The decomposition of the experimental spectra can be used to investigate the effect of specimen orientation on the " quantified result.