J.W. Milnor wrote an important article titled ”On manifolds homeomorphic to the 7-sphere”. This article shows the existence of an exotic differential structure on the 7-sphere. The aim of this work is to explain Milnor's article, and to reach this expectation we introduce differential theory and try to make clear the notion of Pontrjagin classes. Finally, a short introduction to Morse theory is added to give a wider point of view on the problematic.