What is the prerequisite knowledge for learning Galois theory?

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.

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.