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, János Kollár; 9. Non-klt techniques, Florin Ambro; 10. Glossary, Alessio Corti; Bibliography; Index