  I discuss in this talk mainly three topics related with dark matter motivated
neutrino mass spectrum and a generic issue of mass pattern, the normal versus
the inverted mass hierarchies. In the first part, by describing failure of a
nontrivial potential counter example, I argue that the standard 3 $\nu$ mixing
scheme with the solar and the atmospheric $\Delta m^2$'s is robust. In the
second part, I discuss the almost degenerate neutrino (ADN) scenario as the
unique possibility of accommodating dark matter mass neutrinos into the 3 $\nu$
scheme. I review a cosmological bound and then reanalyze the constraints
imposed on the ADN scenario with the new data of double beta decay experiment.
In the last part, I discuss the 3 $\nu$ flavor transformation in supernova (SN)
and point out the possibility that neutrinos from SN may distinguish the normal
versus inverted hierarchies of neutrino masses. By analyzing the neutrino data
from SN1987A, I argue that the inverted mass hierarchy is disfavored by the
data.
