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“The book sets out on a project to convey the big ideas of algebraic geometry in the 21st century in a way that will be accessible and that will get to get to the big ideas (relatively) quickly. … The topics … give a good overview of modern algebraic geometry, and I think that a reader who is interested in getting quick statements of theorems will find a lot to like in this book.” (Darren Glass, The Mathematical Association of America, August, 2012)
“The book under review offers a first introduction to algebraic geometry of a special kind … . quite a variety of topics from modern algebraic geometry is presented to the reader, often in a sketchy or survey-like manner, but always with hints for further reading. The sections of the single chapters are mostly short, and the presentation is nowhere lengthy or tedious. … the book must be seen as a charming invitation to algebraic geometry, along some sort of ‘royal road’ (of pleasure and diversity).” (Werner Kleinert, Zentralblatt MATH, Vol. 1237, 2012)