Definition:Absolute Galois Group

Definition
Let $K$ be a field.

Definition 1
The absolute Galois group of $K$ is the Galois group $\operatorname{Gal} \left({K^{\operatorname{sep} } \mid K}\right)$ of its separable closure.

Definition 2
The absolute Galois group of $K$ is the automorphism group $\operatorname{Aut} \left({\overline K \mid K}\right)$ of its algebraic closure.

Also see

 * Equivalence of Definitions of Absolute Galois Group