The fundamental theorem of Galois theory Who proved the modern form of the fundamental theorem of Galois theory?. Was it in the original Galois' manuscript?
 A: Galois's Proposition I (as translated by Edwards) is:
Let the equation be given whose $m$ roots are $a,b,c,\ldots$.  There will always be a group of permuations of the letters $a,b,c,\ldots$ which will have the following property:  1)  that each function invariant under the substitutions of this group will be known rationally; 2) conversely, that every function of these roots which can be determined rationally will be invariant under these substitutions.  
As Edwards observes, it takes a lot of work to decipher the exact meanings of "substitution" and "invariant" here, but once you've done that, this can be translated into modern language as:
If an element of the splitting field of $K(a,b,c,\ldots)$ is left fixed by all the automorphisms of the Galois group then it is in $K$.
The fundamental theorem of Galois theory (i.e. the Galois correspondence) follows easily, though Edwards doesn't say who first stated it.
A: Surely the book 
Edwards, Harold M. Galois theory. Graduate Texts in Mathematics, 101. Springer-Verlag, New York, 1984. xiii+152 pp. ISBN: 0-387-90980-X MR0743418 (87i:12002) (link to amazon) 
would be useful. This book about Galois theory is made from the historical point of view. In particular, it contains an English translation of Galois' memoir. 
A: The modern form can be found in Galois Theory, by Emil Artin and Arthur N. Milgram page 46, published in 1944. I'm not expert in math history, but once, I heard Artin was the first person to wrote the modern account of Galois theory.
A: I am not particularly interested in mathematical history, but Peter Newmann is: http://www.ems-ph.org/books/book.php?proj_nr=137.
