We report near infrared (NIR) spectroscopic observations of twelve ``Branch-normal'' Type Ia supernovae (SNe Ia) which cover the wavelength region from 0.8-2.5 microns. Our sample more than doubles the number of SNe Ia with published NIR spectra within three weeks of maximum light. The epochs of observation range from thirteen days before maximum light to eighteen days after maximum light. A detailed model for a Type Ia supernovae is used to identify spectral features. The Doppler shifts of lines are measured to obtain the velocity and, thus, the radial distribution of elements. The NIR is an extremely useful tool to probe the chemical structure in the layers of SNe Ia ejecta. This wavelength region is optimal for examining certain products of the SNe Ia explosion that may be blended or obscured in other spectral regions. We identify spectral features from MgII, CaII, SiII, FeII, CoII, NiII and possibly MnII. We find no indications for hydrogen, helium or carbon in the spectra. The spectral features reveal important clues about the physical characteristics of SNe Ia. We use the features to derive upper limits for the amount of unburned matter, to identify the transition regions from explosive carbon to oxygen burning and from partial to complete silicon burning, and to estimate the level of mixing during and after the explosion.

44 pages, 7 figures, 3 tables, accepted by ApJ