The Galois correspondence
The main result in classical Galois theory is the Galois correspondence which we look at in this video. This relates intermediate fields of a finite extension K/F with subgroups of the corresponding Galois group. When K/F is Galois, this relation is an actual bijection which reverses inclusions. This means that by studying the finite Galois group, we can learn a lot about the field extension. We give some applications, including a proof of the primitive element theorem stating that finite separable extensions can be generated by a single (primitive) element.