  We employ the Ricci flow to derive a new theorem about Gromov almost flat
manifolds, which generalizes and strengthens the celebrated Gromov--Ruh
Theorem. In our theorem, the condition $diam^2 |K| \leq \epsilon_n$ in the
Gromov--Ruh Theorem is replaced by the substantially weaker condition
$\|Rm\|_{n/2}$ $ C_S^2 \leq \varepsilon_n$.
