Background to start Galois theory I have been taking Abstract Algebra graduate classes, and we will begin studying Galois theory.
However, since it is a graduate-level course, the teacher has assumed everyone already had taken undergrauate-level algebra. Problem is, I come from an Engineering background, which did not have it.
Needless to say, I am a bit lost on what I need to know. The teacher will do a brief revision on fields, but I do not even know much about rings (I am fairly comfortable with groups though, since we studied it).
So, long story short, my question is: What do I absolutely must know about rings and fields to understand Galois theory?
I would also appreciate any references that may help. I have been reading Artin's Algebra, and Goodman's Algebra: Abstract and Concrete for now.

And, just to clarify, I do intend to learn more about Algebra later on. It is just that I need to keep up with the lectures, so I must learn the necessary things in a really short time.
 A: OK, I think my question might be wandering in the not-answered list of questions, so I'll share my thoughts. 
A good book I've been using is Gallian's Contemporary Abstract Algebra. It is very well organized, and has a good number of examples and exercises (some solved). Irrelevant to the actual content, but I also liked the biographies of some mathematicians, which can be an inspirational breather.

From what I've seen, you need some knowledge about rings and especially ideals. Integral domains and unique factorization domains play some roles here and there. Also, a very strong knowledge and familiarity of fields and extension fields is highly desirable.
Group theory is also important, but I've been studying these a lot (even if only because of a test).
Specific topics you want to be familiar with are the symmetric group and especially polynomial rings. This last one can't be emphasized enough, in my opinion, but I think it suffices to say that they were the main motivation for the development of Galois Theory.
