I hope this is the right forum for this question. Over the summer I would like to rigorously study the type of algebraic geometry that plays a role in things like string theory. My mathematics background is that I just completed the first year grad sequence (differential topology, algebraic topology, lots of algebra, real and complex analysis). I am thinking of going through some of Griffiths and Harris's Principles of Algebraic Geometry: does this cover most of the relevant material? One problem with it (besides its difficulty) is that it has no exercises. Is there a similar book with problems or are there related problems I can find online somewhere? Thanks!