Robin Hartshorne

In the same bucket as Lang - this is a classic of mathematics, but is marginally unreadable and definitely unsuitable for the beginner. It does have everything, though, and the exercises are great.

I struggled through its first three chapters during two grad courses at UIUC. I didn't quite understand what I was doing at the very end but I found the whole thing enjoyable and sometimes even fun.

This is the main reference when it comes to Algebraic Geometry. It's brief and it goes to the point. It's not an encyclpedia but a text book. I recommend it mixed with a few pieces from Shafarevich and Mumford, a good book on commutative algebra (I use Atiyah's), and some salt.

Oh! And remember: show more If you don't find a certain basic result, it's one of the exercises. show less

This book is a guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment.