Birational geometry of surfaces and threefolds

We will consider basics of birational geometry of surfaces and 3-folds with special regard to problems of rationality. The tentative plan of the lectures is the following:
Lecture 1. Blow ups, blow downs, canonical class, adjunction formula, rational surfaces, rationality criterion, quadric surfaces, cubic surfaces, two-dimensional Minimal Model Program, surfaces with a finite group action, surfaces over algebraically non-closed field of characteristic zero.
Lecture 2. Singularities of pairs, log canonical singularities, Kawamata log terminal singularities, mobile log pairs, canonical singularities, Nadel-Shokurov vanishing theorem, Inversion of Adjunction and its applications, Noether-Fano inequality, Pukhlikov inequality, Corti inequality.
Lecture 3. Non-rational surfaces over algebraically non-closed fields, non-rationality of smooth quartic 3-folds, finite subgroups in Cremona groups.