This thesis is broken down into 4 major sections, each highlighting a different way with which to use spectrum synthesis to analyze SNe Ia. Chapters 2 and 3 look at normal SNe Ia and their potential use as distance indicators using SEAM. Chapter 4 examines spectral correlations with luminosity in SNe Ia and provides a plausible explanation for these correlations via spectrum synthesis. In Chapter 5 the spectra of various hydrodynamical models are calculated in an effort to answer the question of which current progenitor/explosion model is the most plausible for a SN Ia. Finally, we look at the importance of NLTE calculations and line identifications in Chapter 6. Also included are two appendices which contain more technical information concerning γ-ray deposition and the thermalization parameter.

Type Ia supernovae (SNe Ia) are valuable distance indicators for cosmology and the elements they eject are are important for nucleosynthesis. They appear to be thermonuclear disruptions of carbon-oxygen white dwarfs that accrete from companion stars until they approach the Chandrasekbar mass, and there is a suspicion that the propagation of the nuclear burning front involves a transition from a deflagration to a detonation. Detailed modeling of the atmospheres and spectra of SNe Ia is needed to advance our understanding of SNe Ia. Comparison of synthetic and observed spectra provides information on the temperature, density, velocity, and composition of the ejected matter and thus constrain hydrodynamical models. In addition, the expanding photosphere method yields distances to individual events that are independent of distances based on the decay of \sp56Ni in SNe Ia and of Cepheid variable stars in the parent galaxies.