Abstract : The objective of this thesis is to achieve a better understanding properties of different phases of titanium. The study of titanium im- bearing the fundamental point of view because the understanding of the elements corresponding to the filling of the 3d shell is still far from satisfactory tory. Titanium is one of the first transition elements. He has still reasonable numbers of electrons model, while presenting difficulties in modeling the 3d shell. When problems modeling encountered are not specifically related to titanium, but represent a general trend among the transition elements, we extend our analysis to other materials such as titanium dioxide, copper and zirconium.