We present a short proof of the Albert-Brauer-Hasse-Noether theorem on the Brauer group of a global field. The connection between Galois cohomology and algebraic tori theory is emphasized. Let $K/k$ be a finite Galois extension of arbitrary fields with group $G$, then the relative Brauer group is $Br(K/k)\simeq H^2(G,K^*) \simeq H^1(G,T_1 (K))$, where $T_1$ is the algebraic $k$-torus associated to the augmentation ideal $I_G$ of $G$. When $k$ is a global field, we use fundamental facts from algebraic tori theory, Tate-Nakayama duality and modern versions of Grunwald-Wang's lemma to deduce the short exact sequence $O\longrightarrow Br(k) \longrightarrow \oplus Br(k_v)\longrightarrow \mathbb {Q}/\mathbb {Z}\longrightarrow 0.$ where $k_v$ runs over the completions of $k$ at all places $v$ of $k$.