Self-Studying Abstract Algebra; Aye or Nay? I am a high schooler with a deep interest in mathematics, which is why I have self-studied Linear Algebra and have begun my self-study in Differential Equations. As I am a man who likes to plan ahead, I'm pondering what field of mathematics to plunge into once I've finished DE's. I am thinking of Abstract Algebra: it has always sounded mystical and intruiging to me for some reason. I have a couple of questions regarding AA:


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*What exactly is Abstract Algebra? What does it study? Please use your own definition, no wikipedia definition please.

*What are its applications? Does it have a use for example in physics or chemistry, or is it as abstract as its name suggests?

*Would it be a logical step for a high schooler to self-study abstract algebra after studying LA and DE's, or is there a field of (post-high school) math 'better' or more useful to study prior to abstract algebra?

*What are some good books, pdfs, open courseware etc. on abstract algebra? links and names please. 

A friend of mine showed me this free abstract algebra book (Abstract Algebra: Theory and Applications by Judson) a while back. It's fairly recent, and looks reasonably comprehensive enough. I admit, I haven't read the entire thing, but it seems like it would be a good starting point.
http://abstract.ups.edu/index.html
It contains applications as well, which I haven't seen very much in introductory abstract algebra texts.
