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This book by Robin Hartshorne is intended to introduce graduate students to the methods and results of modern algebraic geometry. The book contains numerous exercises which include important theorems, additional examples and alternate treatments of some topics. The text is very good at introducing a very difficult subject to graduate students who want to work in the field.

I chose this book because it was the text that I used to first learn algebraic geometry and I spent many hours on the wonderful and challenging exercises in this book.