Cremona Transformations

Hilda Hudson's book, first published in 1927, is the classic work on Cremona transformations. Her complete and elegant treatment of Cremona transformations of the plane in Part I was a central influence on 20th century work in algebraic geometry, singularity theory and algebra, and continues to inspire new research. Part II of the book, on 3-fold birational geometry, is more in the nature of a pioneering foray; current advances in higher dimensional geometry (Mori theory) provide for the first time adequate tools to discuss general cases of 3-fold birational transformations. This timely reissue of Hudson's book links ancient and modern algebraic geometry: its bibliography and historical sketch make the book an indispensable guide to the extensive early literature, while the detailed treatment of particular cases and the many unsolved questions on 3-fold birational geometry it raises present worthy challenges to current and future generations of 3-folders.