  Coherent states $(CS)$ of the $SU(N)$ groups are constructed explicitly and
their properties are investigated. They represent a nontrivial generalization
of the spining $CS$ of the $SU(2)$ group. The $CS$ are parametrized by the
points of the coset space, which is, in that particular case, the projective
space $CP^{N-1}$ and plays the role of the phase space of a corresponding
classical mechanics. The $CS$ possess of a minimum uncertainty, they minimize
an invariant dispersion of the quadratic Casimir operator. The classical limit
is ivestigated in terms of symbols of operators. The role of the Planck
constant playes $h=P^{-1}$, where $P$ is the signature of the representation.
The classical limit of the so called star commutator generates the Poisson
bracket in the $CP^{N-1}$ phase space. The logarithm of the modulus of the $CS$
overlapping, being interpreted as a symmetric in the space, gives the
Fubini-Study metric in $CP^{N-1}$. The $CS$ constructed are useful for the
quasi-classical analysis of the quantum equations of the $SU(N)$ gauge
symmetric theories.
