Amnon Neeman is professor of mathematics at Australian National University. He is the author of the book Triangulated Categories.
All in all, the book under review is a masterpiece of expository writing in modern algebraic geometry. It is exactly what the author promised: no comprehensive text to train future algebraic geometers, but rather an attempt to convince students of the fascinating beauty, the tremendous power, and the high value of the methods of algebraic and analytic geometry ... The author has reached his declared goal in an admirable, truly brilliant manner. His lucid exposition of these modern, fairly advanced topics in the field for beginners breathes his passion for the subject and for grippingly teaching it, and his style of writing bespeaks a good sympathetic understanding of students and their needs. Numerous synoptic sections, asides for the expert reader, and additional remarks help the student grasp the vast material thoroughly, and both the careful glossary and the detailed index facilitate active work with this highly inspiring book. Also, the author makes concrete, instructive proposals for how to use his text for different variants of self-study or teaching, which is particularly useful as its current extended contents now offer far more than can be covered in a one-semester course ... It remains to wish that this very special introduction to the realm of(complex)algebraic geometry finds deserved wide-spread interest within the mathematical community. Werner Kleinert, Zentralblatt MATH