Type Ia Supernovae (SNe Ia) have an important role to measure a distance to an anonymous galaxy because they have a good correlation of the decline rates of the light curves with the absolute luminosity. However, there are several unresolved problems despite of having such important backgrounds. Recently, new kinds of diversity of SNe Ia have been discovered by optical observations. First, super-Chandrasekhar SNe which have extremely high luminosity, slow decline rate of the light curves, slow expansion velocity and strong carbon features. These characteristics are not seen in typical SNe Ia. The total ejected mass could significantly exceed Chandrasekhar-limiting mass for the white dwarf. I would like to introduce our observational study of a super-Chandra SN 2009dc. As another example of diversity of SNe Ia, I would like also to introduce Type Iax SNe. Their absolute luminosity is much fainter than those expected from their light curves in spite of the fact that their spectra exhibit SNe Ia-like features. Recently, direct detection of a progenitor candidate on the pre-discovery images for Type Iax SN 2012Z are reported. I would like to introduce the follow-up observations of SN 2012Z with Optical and Infrared Synergetic Telescopes for Education and Research (OISTER) and 8.2m Subaru telescope.