How much group theory is required before undertaking an introductory course on Galois Theory?

Question

How much knowledge of group theory is needed in order to begin Galois Theory? Which topics are most relevant?

Answer 1

Most Galois Theory books are self-explanatory, but you need to familiarize yourself with concepts as solvable groups (this relates to equations being solvable by radicals), simple groups. Also Sylow theory helps a lot. In addition, knowledge of rings and fields is necessary.

By the way, Ian Stewart's book Galois Theory makes a very nice read.

Answer 2

Some elementary: definitions and examples of groups (of small orders and especially $S_n,A_n$), normal subgroups, cyclic and abelian groups, quotient groups, isomorphism theorem.

[These of these terminologies enter in the (two) main theorems of Galois; examples are needed to know just to understand what is going on].