Physics of SNeIa and Cosmology

We give an overview of the current understanding of Type Ia supernovae relevant for their use as cosmological distance indicators. We present the physical basis to understand their homogeneity of the observed light curves and spectra and the observed correlations. This provides a robust method to determine the Hubble constant, 67 +- 8 (2 sigma) km/Mpc/sec, independently from primary distance indicators. We discuss the uncertainties and tests which include SNe Ia based distance determinations prior to delta-Ceph. measurements for the host galaxies. Based on detailed models, we study the small variations from homogeneities and their observable consequences. In combination with future data, this underlines the suitability and promises the refinements needed to determine accurate relative distances within 2 to 3 % and to use SNe Ia for high precision cosmology.