We describe a research program to improve the understanding of Type Ia Supernovae (SNe Ia) by modeling and observing near infrared (NIR) spectra of these events. The NIR between 0.9 microns and 2.5 microns is optimal for examining certain products of the SNe Ia explosion that may be blended or obscured in other spectral regions. NIR analysis will enable us to place important constraints on the physical properties of SNe Ia progenitors and their explosion dynamics. These are critical steps toward understanding the physics of Type Ia Supernovae. We have identified features in NIR spectra of SNe Ia that discriminate between Population I and Population II progenitors. These features can significantly restrict the evolutionary history of SNe Ia. We also examine certain products of the nuclear burning that enable us to place constraints on the propagation of nuclear burning during the explosion, and on the behavior of the burning front during the event. We will be able to differentiate between the several explosion models for SNe Ia.