Observations indicate that Type Ia supernovae (SNe Ia) can be arranged in a sequence ranging from peculiar powerful explosions like SN 1991T through the nearly homogeneous normal ones like SN 1981B and 1989B to peculiar weak events like SN 1991bg. The powerful SNe Ia are observationally and intrinsically uncommon, the normal ones are observationally and intrinsically common, and weak events are observationally uncommon but intrinsically common. SNe Ia appear to be thermonuclear disruptions of carbon-oxygen white dwarfs that involve a ''delayed detonation'', in which a subsonic deflagration flame becomes a supersonic detonation. This mechanism may account for both normal and weak SNe Ia in terms of white dwarfs at (or above) the Chandrasekhar mass. The unique SN 1991T remains enigmatic. On the basis of one astronomical (Cepheid) and two astrophysical (Ni-56-powered light curves, expanding photosphere method) determinations of SN Ia absolute magnitudes we conclude that the value of the Hubble constant is low, H-0 similar or equal to 50-60 km s(-1) Mpc(-1). Determining the value of the cosmic deceleration parameter, q(0), by means of SNe Ia appears to be feasible.