  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.
