  The abundance distribution of the elements in the ejecta of the peculiar,
luminous Type Ia supernova (SN Ia) 1991T is obtained modelling spectra from
before maximum light until a year after the explosion, with the method of
"Abundance Tomography". SN 1991T is different from other slowly declining SNe
Ia (e.g. SN 1999ee) in having a weaker Si II 6355 line and strong features of
iron group elements before maximum. The distance to the SN is investigated
along with the abundances and the density profile. The ionization transition
that happens around maximum sets a strict upper limit on the luminosity. Both
W7 and the WDD3 delayed detonation model are tested. WDD3 is found to provide
marginally better fits. In this model the core of the ejecta is dominated by
stable Fe with a mass of about 0.15 solar masses, as in most SNe Ia. The layer
above is mainly 56Ni up to v~10000 km/s (~0.78 solar masses). A significant
amount of 56Ni (~3 %) is located in the outer layers. A narrow layer between
10000 km/s and ~12000 km/s is dominated by intermediate mass elements (IME),
~0.18 solar masses. This is small for a SN Ia. The high luminosity and the
consequently high ionization, and the high 56Ni abundance at high velocities
explain the peculiar early-time spectra of SN 1991T. The outer part is mainly
of oxygen, ~0.3 solar masses. Carbon lines are never detected, yielding an
upper limit of 0.01 solar masses for C. The abundances obtained with the W7
density model are qualitatively similar to those of the WDD3 model. Different
elements are stratified with moderate mixing, resembling a delayed detonation.
