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 Horing, Zentralblatt MATH, Vol. 1204, 2011)

• Basics.- Preliminaries.- Singularities.- Recent advances in the minimal model program.- The main result.- Multiplier ideal sheaves.- Finite generation of the restricted algebra.- Log terminal models.- Non-vanishing.- Finiteness of log terminal models.- Compact moduli spaces of canonically polarized varieties.- Moduli problems.- Hilbert schemes.- The construction of the moduli space.- Families and moduli functors.- Singularities of stable varieties.- Subvarieties of moduli spaces.

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 Horing, Zentralblatt MATH, Vol. 1204, 2011)

• Basics.- Preliminaries.- Singularities.- Recent advances in the minimal model program.- The main result.- Multiplier ideal sheaves.- Finite generation of the restricted algebra.- Log terminal models.- Non-vanishing.- Finiteness of log terminal models.- Compact moduli spaces of canonically polarized varieties.- Moduli problems.- Hilbert schemes.- The construction of the moduli space.- Families and moduli functors.- Singularities of stable varieties.- Subvarieties of moduli spaces.