When was the modern field theory approach to Galois theory developed?

Question

It is well known that Galois, and other mathematicians around that time, considered Galois groups to be permutation groups and approached Galois theory in this manner. At some point the theory took a different angle and it was approached using newly developed field theory. The study of roots of the polynomials was approached with splitting fields etc. This gave a better and more concise statement of the fundamental theory of Galois theory. At which point did this modern approach arise?

Answer 1

A first general treatment (that is, with an abstract notion of field, which is how I understand the question) of Galois theory was given by Heinrich Weber in "Die allgemeinen Grundlagen der Galois'schen Gleichungstheorie" Mathematische Annalen 43 (1893) 548 - 549