  Under certain general conditions, we prove that the stable central limit
theorem holds in the total variation distance and get its optimal convergence
rate for all $\alpha \in (0,2)$. Our method is by two measure decompositions,
one step estimates, and a very delicate induction with respect to $\alpha$. One
measure decomposition is light tailed and borrowed from \cite{BC16}, while the
other one is heavy tailed and indispensable for lifting convergence rate for
small $\alpha$. The proof is elementary and composed of the ingredients at the
postgraduate level. Our result clarifies that when $\alpha=1$ and $X$ has a
symmetric Pareto distribution, the optimal rate is $n^{-1}$ rather than $n^{-1}
(\ln n)^2$ as conjectured in literatures.
