To start with:

Galois Groups and Fundamental Groups, by Tamás Szamuely (The theorem in section 3.4 about the absolute Galois group go $\mathbb{C}(t)$ is amazing and enlightening.)

And then:

Milne, James S. (1980), Étale cohomology, Princeton Mathematical Series 33, Princeton University Press

Deligne, Pierre, ed. (1977), Séminaire de Géométrie Algébrique du Bois Marie — Cohomologie étale (SGA 41⁄2), Lecture notes in mathematics (in French) 569