Typically, when one first learns Galois theory, the approach is to fix a field like $\mathbb Q$ and study a finite Galois extension $K/{\mathbb Q}$. It turns out the right approach is to study all finite Galois extensions simultaneously, that is consider $Gal( \bar{ \mathbb Q}/{\mathbb Q})$. In this talk I will explain what this group is, how little we know about it, and how “understanding” it has been helpful in solving some big problems in Number Theory.