A large part of this book is a digest of the great work of Shokurov [Sho03]: in particular, we give a complete and essentially self-contained construction of 3-fold and 4-fold kit flips.Shokurov has introduced many new ideas in the field and has made huge progress on the construction of higher dimensional flips. However. [Sho03] is very difficult to understand: in this book, we rewrite the entire subject from scratch.

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