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.