We are engaged in a comprehensive program to find reliable elemental abundances in and to probe the physical structure of the Orion Nebula, the brightest and best-resolved HII region. This thesis assists in the fulfillment of this goal by analysing, in detail, deep echelle spectra and HST spectra (FOS, STIS) of various lines of sight in the nebula.

All observed fluxes are affected by extinction, mostly from the foreground "veil", and so it is essential that they be corrected accurately before further analysis and interpretation. An analytic expression for the wavelength dependence of the extinction is developed which when normalized for a given line of sight provides a solid basis for the extinction correction from the ultraviolet through to the infrared.

Applying our new analytic extinction correction to ground- and space-based spectral observations, we are able to confirm - for the first time - a number of the theoretically-expected deviations from He iIcase B recombination theory. Furthermore, we show that CLOUDY models that include radiative transfer effects provide a remarkable quantitative agreement between theory and observation.

Ionic abundances can be derived from permitted and forbidden lines with knowledge of the dominant line formation mechanism. However, for a given ion, the derived abundances are not consistent. Temperature fluctuations within the nebula have been invoked to reconcile these differences. From temperature measurements using long-slit STIS spectra we find that actual temperature fluctuations in the plane of the sky are minimal.

The nebula is home to a number of velocity systems, both within the nebula's primary ionization front and elsewhere. Our high-resolution ground-based echelle spectra allow for the isolation of many of these velocity systems, including the distinctive velocity-shifted spectrum associated with a Herbig-Haro object, HH 529. By modeling its emission lines, we determine a gas-phase abundance of Fe that is consistent with the depleted (relative to solar) abundance found in the Orion Nebula - evidence for the presence of dust. We also exploit the nebular velocity structure to show that it is necessary to modify the ground configuration energy levels of O+. Using planetary nebulae and our Orion Nebula observations of the [O II] forbidden lines, we publish new laboratory wavelengths for these same lines.