  We compute the quantum cohomology ring $H^*_{\varphi}({\bf P}, {\bf C})$ of
an arbitrary $d$-dimensional smooth projective toric manifold ${\bf
P}_{\Sigma}$ associated with a fan $\Sigma$. The multiplicative structure of
$H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ depends on the choice of an element
$avarphi$ in the ordinary cohomology group $H^2({\bf P}_{\Sigma}, {\bf C})$.
There are many properties of the quantum cohomology rings $H^*_{\varphi}({\bf
P}_{\Sigma}, {\bf C})$ which are supposed to be valid for quantum cohomology
rings of K\"ahler manifolds
