This edited collection of chapters, authored by leading experts, provides a complete and essentially self-contained construction of 3-fold and 4-fold klt flips. A large part of the text is a digest of Shokurov's work in the field and a concise, complete and pedagogical proof of the existence of 3-fold flips is presented. The text includes a ten page glossary and is accessible to students and researchers in algebraic geometry.

1. Introduction, Alessio Corti 2. 3-fold flips after Shokurov, Alessio Corti 3. What is log terminal?, Osamu Fujino 4. Special termination and reduction to pl flips, Osamu Fujino 5. Extension theorems and the existence of flips, Christopher Hacon and James McKernan 6. Saturated mobile b-divisors on weak del Pezzo klt surfaces, Alessio Corti, James McKernan, and Hiromichi Takagi 7. Confined divisors, James McKernan 8. Kodaira's canonical bundle formula and adjunction, Janos Kollar 9. Non-klt techniques, Florin Ambro 10. Glossary, Alessio Corti Bibliography Index