  Spectroscopic and photometric evidence indicates that Type Ia supernovae (SNe
Ia) are the thermonuclear explosions of accreting white dwarfs. However, the
progenitor binary systems and hydrodynamical models for SNe Ia are still
controversial. The relatively uniform light curves and spectral evolution of
SNe Ia have led to their use as a standard candle for determining cosmological
parameters, such as the Hubble constant, the density parameter, and the
cosmological constant. Recent progress includes the calibration of the absolute
maximum brightness of SNe Ia with the Hubble Space Telescope, the reduction of
the dispersion in the Hubble diagram through the use of the relation between
the light curve shape and the maximum brightness of SNe Ia, and the discovery
of many SNe Ia with high red shifts.
