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:
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.