  We provide an abstract multivariate central limit theorem with the
Lindeberg-type error bounded in terms of Lipschitz functions (Wasserstein
1-distance) or functions with bounded second or third derivatives. The result
is proved by means of Stein's method. For sums of i.i.d. random vectors with
finite third absolute moment, the optimal rate of convergence is established
(that is, we eliminate the logarithmic factor in the case of Lipschitz test
functions). We indicate how the result could be applied to certain other
dependence structures, but do not derive bounds explicitly.
