  SDE driven by an $\alpha $-stable process, $\alpha \in \lbrack 1,2),$ with
Lipshitz continuous coefficient and $\beta $-H\"older drift is considered. The
existence and uniqueness of a strong solution is proved when $\beta >1-\alpha
/2$ by showing that it is $L_{p}$-limit of Euler approximations. The
$L_{p}$-error (rate of convergence) is obtained for a nondegenerate truncated
and nontruncated driving process. The rate in the case of Lipshitz continuous
coefficients is derived as well.
