What is the prerequisite knowledge for learning Galois theory? What is the prerequisite knowledge for learning Galois theory? I don't know what a ring is.
 A: Try also these excellent books:


*

*Field theory and its classical problems by Hadlock.

*Galois Theory for Beginners: A Historical Perspective by Bewersdorff.

*Galois' Theory of Algebraic Equations by Tignol.
and also


*

*Galois Theory for Beginners by 
John Stillwell, 
The American Mathematical Monthly, Vol. 101, No. 1 (Jan., 1994), pp. 22-27.

A: If you don't know a great deal of abstract algebra so far, maybe "A First Course in Abstract Algebra" by Fraleigh might be a good place to start, as it includes all the prerequisites (groups, rings, fields, linear algebra) as well as a very readable treatment of Galois Theory itself.
A: Read Galois Theory, Rotman, Springer 1998, as a first step.
Summing over the comments below, one could conclude that a necessary prerequisite is the collection of such theories as groups, rings, fields, and linear algebra. Of course one needs to know what a field is, and what a group is, before you learn Galois theory; also, the use of linear algebra appears almost everywhere. In fact, I think those should suffice for a first-time exposition to the theory. Indeed, familiarity grows with time one spends in practicing the theory.
