  Generalized coherent states are developed for SU(n) systems for arbitrary
$n$. This is done by first iteratively determining explicit representations for
the SU(n) coherent states, and then determining parametric representations
useful for applications. For SU(n), the set of coherent states is isomorphic to
a coset space $SU(n)/SU(n-1)$, and thus shows the geometrical structure of the
coset space. These results provide a convenient $(2n - 1)$--dimensional space
for the description of arbitrary SU(n) systems. We further obtain the metric
and measure on the coset space, and show some properties of the SU(n) coherent
states.
