  The notion of the supercharacter theory was introduced by P.Diaconis and
I.M.Isaaks in 2008. In this paper we review the main statements of the general
theory, we observe the construction of supercharacter theory for algebra groups
and the theory of basic characters for the unitriangular groups over the finite
field. Basing on the previous papers of the author, we construct the
supercharacter theory for the finite groups of triangular type. We characterize
the structure of Hopf algebra of supercharacters for the triangular group over
the finite field.
