  Theoretical monochromatic light curves and photospheric expansion velocities
are compared with observations of 27 Type Ia supernovae (SNe Ia). A set of 37
models has been considered which encompasses all currently discussed explosion
scenarios for Type Ia supernovae including deflagrations, detonations, delayed
detonations, pulsating delayed detonations and tamped detonations of Chandra-
mass, and Helium detonations of low mass white dwarfs. The explosions are
calculated using one-dimensional Lagrangian hydro and radiation-hydro codes
with incorporated nuclear networks. Subsequently, light curves are constructed
using our LC scheme which includes an implicit radiation transport, expansion
opacities, a Monte-Carlo $\gamma $-ray transport, and molecular and dust
formation. For some supernovae, results of detailed non-LTE calculations have
been considered.
  Observational properties of our series of models are discussed, the relation
between the absolute brightness, post-maximum decline rates, the colors at
several moments of time, etc. All models with a Ni production larger than 0.4
solar masses produce light curves of similar brightness. The influence of the
cosmological red shift on the light curves and on the correction for
interstellar reddening is discussed.
  Based on data rectification of the standard deviation, a quantitative
procedure to fit the observations has been used to the determine the free
parameters, i.e. the correct model, the distance, the reddening, and the time
of the explosion. The results are discussed in detail and applied to determine
Ho and qo.
