  We present a classification theorem for a class of unital simple separable
amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class
of simple $C^*$-algebras exhausts all possible Elliott invariant for unital
stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras.
Moreover, it contains all unital simple separable amenable $C^*$-alegbras which
satisfy the UCT and have finite rational tracial rank.
