Abstract: I will start with a brief review on quantization theory including the ideas of deformation quantization of Poiison manifolds and Weak quantization approach reviewing the related theorems of Weyl, Wigner, Egorov, Groenewold, Lichnerowitz, Fedosov, Kontsevich, etc. Then using the theory of alpha^*- cohomology (defined by myself) as a modified version of alpha-cohomology (introduced partly by Lizzi et all.) I will classify all the quantum behaviors of translation-invariant non-commutative quantum field theories. A junction to the Kontsevich's theorem will be worked out which leads to classification of translation-invariant structures of space-time. I also apply this achievements to generalize the Drinfeld's twisted Poincare symmetry of translation-invariant non-commutative quantum field theories.