An overview on real division algebras

 In this paper,  we expose initial  concepts of real division algebras, providing historical notes on $\R$, $\C$, $\Ham$ and $\Oct$. This is done to emphasize  the relevance of topological K-theory through the Bott-Milnor-Kervaire Theorem,  which is at the end. For completeness, we also present some classical  results about the main  algebras.