  We shall explain here an idea to generalize classical complex analytic
Kleinian group theory to any odd dimensional cases. For a certain class of
discrete subgroups of $\PGL_{2n+1}(\C)$ acting on $\P^{2n+1}$, we can define
their domains of discontinuity in a canonical manner, regarding an
$n$-dimensional projective linear subspace in $\P^{2n+1}$ as a point, like a
point in the classical $1$-dimensional case. Many interesting (compact)
non-K\"ahler manifolds appear systematically as the canonical quotients of the
domains. In the last section, we shall give some examples.

Complex Variables