Absolute Galois group ($G_K=\mathrm{Gal}(K^{\mathrm{sep}}/K)$)

The absolute Galois group of a field $K$ is $G_K=\mathrm{Gal}(K^{\mathrm{sep}}/K)$. It is a profinite group, the inverse limit of the Galois groups of finite Galois extensions. Its continuous actions on discrete modules are the coefficients for Galois cohomology.