TITLE: Why study Algebraic Geometry?
QUESTION [241 upvotes]: I'm going to start self-stydying algebraic geometry very soon. So, my question is why do mathematicians study algebraic geometry? What are the types of problems in which algebraic geometers are interested in? And what are some of the most beautiful theorems in algebraic geometry?

REPLY [8 votes]: The first chapter of Justin Smith's Introduction to Algebraic Geometry has a nice discussion of Bezout's Theorem and how algebraic geometry approaches geometric problems in general. I think you can download the PDF from the author's web site for free.