TITLE: Undergraduate roadmap to algebraic geometry?
QUESTION [41 upvotes]: Hello,
I'm sorry if this question isn't posted correctly. I hope that it is (since other questions regarding roadmaps have been allowed). Now to my question:
From what I've heard from professors and such, algebraic geometry seems like an interesting branch of mathematics. I'd like to learn some basic results and maybe do some kind of thesis in a few years on the subject. So, what I'm curious about is you have any tips on what books to read? Say that one has read Artin's Algebra and Herstein's Topics in Algebra, and also has the basic courses in real analysis and topology, complex variables etc. down, where should one go to learn? What books? I'm also curious if algebraic geometry (at an "easy level") requires deep knowledge about other fields of mathematics too, so that one might have to read books that at first seems to have no relevance to algebraic geometry?
Best regards.

REPLY [6 votes]: I think the best way is to read a book on commutative algebra (Atiyah & MacDonald) and then, you can start reading Hartshorne's. Chapter 1 will give you a fairly concrete idea of what classical alg. geo. is about. You should also try to do all the exercises even though that will be time consuming. I think this is the best way one can do it.