ABSTRACT
Having seen how Galois Theory works in the context assumed by its inventor, we now begin to generalise everything to a much broader context. Instead of subfields of C, we can consider arbitrary fields. With the increased generality, new phenomena arise, and these must be dealt with. We concentrate on developing this abstract machinery, which centres on the properties of field extensions, especially finite ones. We construct the algebraic closure of a field, in which every polynomial splits into linear factors.
