Abstract:  In the classification of algebraic surfaces, Kodaira’s canonical bundle formula plays an important role. It is natural to expect that some general kinds of canonical bundle formula (quasi-log canonical theory in slightly different language) will play a similar role in the study of higher dimensional varieties.  In this talk, I will try to explain the relative set-up and report some recent results on this direction.  Some of my results are jointed works with Osamu Fujino.