What was Galois theory like before Emil Artin? I read that the primitive element theorem for fields was fundamental in expositions of Galois theory before Emil Artin reformulated the subject. What are the differences between pre and post-Artin Galois theory?
 A: Two articles by James Pierpont in the first two issues of the annals of math second series give a view of Galois theory as of 1900.  They are:
Galois' Theory of Algebraic Equations, Ann. of Math. second series, Vol 1 (1899-1900), 113-143, 
and
Galois' Theory of Algebraic Equations. Part II. Irrational Resolvents, Ann. of Math. second 
series, Vol 2 (1900-1901), 22-56.
A: The development of Galois theory from Lagrange to Artin by B. Melvin Kiernan, is a history of pre-Artin Galois theory.
A: Post-Artin, you could read about it in English! No, that's not fair, but few authors writing in English on the "theory of equations" handled it. An exception would be L. E. Dickson, and I looked at one of his books before encountering the so-called modern theory (now aged about 85) of Artin and Emmy Noether, as written up by van der Waerden first. I think I must have read Modern Algebraic Theories by Dickson. Anyway the review of that in Bulletin of the AMS (Bull. Amer. Math. Soc. 32 (1926), 707-710) can give some idea of the good old days, if you can't find the book.
By the way, just anecdotal, but G. H. Hardy made some public blunder in Galois theory, so it wasn't really transparent.
A: it was called "theory of equations" in certain places in English.  one learned how to solve cubic and quartic and other special types. Galois theory was taught literally as the study of symmetric polynomials of the roots - the invariants and coinvariants 
here's one 


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*The theory of equations: with an introd. to the theory of binary algebraic forms Burnside Panton


Galois' own writings are available online.  His total writings total less than 100 pages (only some of it on theory of permutation "groups" for solving equations) and changed the course of mathematics. 


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*Manuscrits de Évariste Galois
