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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, elementaryparticle theory and mathematical physics. Irreducible unitary representationsof the principal continuous and supplementary as well as discrete series wereobtained. Explicit expressions for spherical functions of the group $SO_0(2,1)$are obtained through the Gauss hypergeometric functions. The Wignercoefficients of the group $SO_{0}(2,1)$ were computed and their explicitexpressions using the bilateral series were represented. The results could beused to study the non-degenerate representations of the de Sitter group$SO(3,2)$.

The theory of representations of groups $SO_{0}(2,1)$ and $ISO(2,1)$. Wigner coefficients of the group $SO_{0}(2,1)$