This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to give a detailed account of the proof for the (weak) factorization theorem of birational maps by Abramovich-Karu-Matsuki-W{\l}odarczyk.
A determinant on birational maps of Severi-Brauer surfaces
Birational maps, PBW degenerate flags and poset polytopes
Birational maps of 3-folds
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