  This paper is devoted to the representations of the groups $SO (2,1)$ and
$ISO (2,1)$. Those groups have an important role in cosmology, elementary
particle theory and mathematical physics. Irreducible unitary representations
of the principal continuous and supplementary as well as discrete series were
obtained. Explicit expressions for spherical functions of the group $SO_0(2,1)$
are obtained through the Gauss hypergeometric functions. The Wigner
coefficients of the group $SO_{0}(2,1)$ were computed and their explicit
expressions using the bilateral series were represented. The results could be
used to study the non-degenerate representations of the de Sitter group
$SO(3,2)$.
