This is a good book on important ideas. But it competes with Hartshorne ALGEBRAIC GEOMETRY and that is a tough challenge. It has roughly the same prerequisites as Hartshorne and covers much the same ideas. The three volumes together are actually a bit longer than Hartshorne. I had hoped this would be a lighter, more easily surveyable book than Hartshorne's. The subject involves a huge amount of material, an overall survey showing how the parts fit together could be very helpful, and the IWANAMI SERIES has some terrific, brief, easy to read, overviews of such subjects — which give proof techniques but refer elsewhere for the details of some longer proofs. But it turns out that Ueno differs from Hartshorne in the other direction: He gives more explicit nuts and bolts of the basic constructions. Overall it is easier to get an overview from Hartshorne. Ueno does also give a lot of "insider information" on how to look at things. It is a good book.