Many uncertainties about the physics of Type Ia Supernovae have been revealed in the recent past, and numerous pieces are puzzled together to achieve a complete description of the phenomenon of thermonuclear explosions in the sky. However, very important parts are still missing. In particular, the concept lacks a proper connection between the various evolutionary steps, namely the progenitor scenario, explosion theory, nucleosynthesis from the burning, and the observations. Early time spectra of Type Ia Supernovae naturally contain information about all of these processes and are at the centre of the entire scenario. Appropriate models of that phase can provide the missing link and improve our understanding of this field enormously. The goal of this thesis is to advance new methods to calculate synthetic spectra in order to extract the information contained in the observations more efficiently. Based on a well established radiation transfer code, a new technique called Abundance Tomography is developed to derive the abundance distribution of Type Ia Supernovae ejecta. While previous approaches were limited to the determination of the abundances of specific species in restricted regions of the supernova envelope, here a complete stratified distribution of all major elements is obtained. This method is applied to the very well observed normal SN 2002bo. Combining the early spectra with those of the nebular phase leads to a coverage of the entire ejecta from the centre out to the highest velocities. The abundances derived are used to compute a synthetic bolometric light curve to test the radial distribution of Fe group and intermediate-mass elements. The sampling procedure of the incident radiation field at the lower boundary is modified to obtain a better description of the real situation in Type Ia Supernovae. This improves the overall flux distribution significantly, especially in the red part of the spectrum, where almost no real line opacity is found. Synthetic spectra with this new procedure reproduce the observations much more accurately, as is shown by models of SN 2002er. Hydrogen lines have never been detected convincingly in Type Ia Supernovae spectra. However, using spectra that were observed more than 10 days before maximum light, it is shown that small amounts of hydrogen in the outer parts of the ejecta can explain high velocity line absorptions, seen rather frequently in various objects, e.g. SN 2002dj, SN 2003du, and SN 1999ee. The hydrogen is not claimed to be primordial to the white dwarf but it is rather the effect of the supernova ejecta interacting with circumstellar material, namely the white dwarf's accretion disk build up prior to the explosion. Finally, UV spectra of Type Ia Supernovae are discussed. The ability of the Monte Carlo technique to deal naturally with this wavelength region is proven. Applications are presented by modelling spectra of SN 2001ep and SN 2001eh obtained with the Hubble Space Telescope. The results are discussed in the broader context of Type Ia Supernovae physics: What causes the diversity in the nearby sample? What are the progenitors and how does the explosion work? What is the influence on cosmological models? A detailed knowledge of the abundances, their distribution in the Supernova ejecta, and their ultimate causes delivers the key to these fundamental issues.