  A classification of finite dimensional irreducible representations of the
nonstandard $q$-deformation $U'_q(so_n)$ of the universal enveloping algebra
$U(so(n, C))$ of the Lie algebra $so(n, C)$ (which does not coincides with the
Drinfeld--Jimbo quantized universal enveloping algebra $U_q(so_n)$) is given
for the case when $q$ is not a root of unity. It is shown that such
representations are exhausted by representations of the classical and
nonclassical types. Examples of the algebras $U'_q(so_3)$ and $U'_q(so_4)$ are
considered in detail. The notions of weights, highest weights, highest weight
vectors are introduced. Raising and lowering operators for irreducible finite
dimensional representations of $U'_q(so_n)$ and explicit formulas for them are
given. They depend on a weight upon which they act. Sketch of proofs of the
main assertions are given.
