  For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th
KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able
to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV
hierarchy). The $W$--algebra associated to the \shs\, of the $(n,m)$--th KdV
hierarchy (called $W(n,m)$ algebra) is isomorphic via a Miura map to the direct
sum of $W_m$--algebra, $W_{n+m}$--algebra and an additional $U(1)$ current
algebra. In turn, from the latter, we can always construct a representation of
$W_\infty$--algebra.
