The Lecture Notes collect seven mini-courses presented at the 5th Prague Summer School on Mathematical Statistical Physics that took placeduringtwoweeksofSeptember2006.Aswithprecedingschools, it was aimed at PhD students and young postdocs. The central theme of the volume is what could be called mathematics of phase transitions in diverse contexts. Even though all courses were meant to introduce the reader to recent progress of a particular topic of modern statis- cal physics, attention has been paid to providing a solid grounding by carefully developing various basic tools. One of the...