It is shown that the Homology group F j [F, F ] of the Complex Analytic Manifold X, wherc F is the Fundamental group of X and [F, F ] the Commutator subgroup, is isomo^hîc to the Co- homology group H°(X, A) of the structure restricted sheaf of X. while [F, F] determines as the normal covering space of X, i. e., the homology covering space of X. In this paper, we investigate therefore the relationship of the Homology group of the complex analytie manifold X to the Cohom- ology group H'’(X,^) of its structure restricted sheaf A.