  The space ${\mathcal A}$ of almost complex structures on a closed manifold
$M$ is studied. A natural parametrization of the space ${\mathcal A}$ is
defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex
weak Pseudo-Riemannian manifold. A curvature of the space ${\mathcal A}$ is
found. The space ${\mathcal A}_\omega$ of associated almost complex structures
on a symplectic manifold $M,\omega$ and space ${\mathcal AO}$ of orthogonal
almost complex structures on a Riemannian manifold $M,g_0$ are considered in
more detail.
