  This paper considers the question of the rate of convergence to ${\alpha}$-
stable laws, using arguments based on the Zolotarev distance to prove bounds.
We provide a rate of convergence to ${\alpha}$-stable random variable where 1 <
${\alpha}$ < 2, in the generalized CLT, that is, for the partial sums of
independent identically distributed random variables which are not assumed to
be square integrable. This work is a technical report based on the Zolotarev
paper in [1].
