  We prove that there exists a positive number $C_{n}$ depending only on $n$
such that for every smooth projective $n$-fold of general type $X$ defined over
{\bf C}, the automorphism group $Aut(X)$ satisfies the inequality
$\sharp{Aut}(X)\leq C_{n}\cdot\mu (X,K_{X})$, where $\mu (X,K_{X})$ is the
volume of $X$ with respect to $K_{X}$.
