  For a finitely generated module $M$, over a commutative Noetherian local ring
$(R, \mathfrak{m})$, it is shown that there exist only a finite number of
non--isomorphic top local cohomology modules
$\mathrm{H}_{\mathfrak{a}}^{\mathrm{dim} (M)}(M)$, for all ideals
$\mathfrak{a}$ of $R$. We present a reduced secondary representation for the
top local cohomology modules with respect to an ideal. It is also shown that
for a given integer $r\geq 0$, if $\mathrm{H}_{\mathfrak{a}}^{r}(R/\mathfrak
{p})$ is zero for all $\mathfrak{p}$ in $\mathrm{Supp}(M)$, then
$\mathrm{H}_{\mathfrak{a}}^{i}(M)= 0$ for all $i\geq r$.
