The dilute magnetic semiconductor (Ga,Mn)As , which is the most interesting and promising material for spintronics applications, has been theoretically studied by using Density Functional Theory. First of all, calculations on GaAs were done and it was found that GaAs is a semiconductor with a direct band gap. The calculated value of the band gap is ~ 0.5eV. Secondly, the material iron was considered and it was confirmed that iron is a ferromagnetic metal with 2.2µB net magnetic moment. Then a magnetic impurity of manganese, Mn was introduced in the nonmagnetic GaAs and it became ferromagnetic with a net magnetic moment of 4µB. The origin of the ferromagnetic behaviour is discussed and also the Curie temperature TC of the material. It appear...