I was reading wikipedia for Galois groups and this term suddenly appears and there is no definition for it.
What is a Galois closure of a field $F$? Does this mean a maximal Galois extension of $F$ so that it merely means a separable closure of $F$?
Secondly, what is a Galois group of an arbitrary extension $E/F$?
Wikipedia states that $Gal(E/F)$ is defined as $Aut(G/F)$ where $G$ is a Galois closure of $E$.
(Since I don't know what Galois closure is, if you don't get bothered, i will add this part after I know what a Galois closure is. Otherwise, I will post another one)