Classification of Higher Dimensional Algebraic Varieties

From the reviews:

“The present text presents the proofs of many results surrounding the minimal model program (MMP) for higher-dimensional varieties. … This text treats the subject in the great generality which is required for getting the most recent results. Hence, it is laden with terminology, all necessary for the modern researcher. … As such, the text will be invaluable for those currently living off of survey articles trying to grasp recent advances in higher-dimensional geometry.” (Michael A. van Opstall, Mathematical Reviews, Issue 2011 f)

“The authors give a detailed account of these new results and the theory of compact moduli spaces of canonically polarised varieties. … the book contains a considerable number of exercises as well as a chapter of hints to solve them. … the authors have made quite an effort to write a text that is both an accessible introduction and a useful reference. … I can only recommend it to researchers and advanced graduate students interested in this highly active field of mathematics.” (Andreas Höring, Zentralblatt MATH, Vol. 1204, 2011)