These notes are a mixture from various sources. They are
- Siegfried Bosch, Algebra: From the Viewpoint of Galois Theory.
- Keith Conrad, https://kconrad.math.uconn.edu/blurbs/.
- Patrick Ingram, Lecture Notes.
- James Milne, Fields and Galois Theory.
- Joseph Rotman, Advanced Modern Algebra.
We aim to cover everything from Ingram's notes but the very last parts about discrete valuation rings, with some additional materials from here and there. We will go to infinite Galois extension if all goes smoothly. Unfortunately, we will not discuss étale algebra.