This book collects the lecture notes of two courses and one mini-course held in a winter school in Bologna in January 2005. The aim of this school was to popularize techniques of geometric measure theory among researchers and PhD students in hyperbolic differential equations. Though initially developed in the context of the calculus of variations, many of these techniques have proved to be quite powerful for the treatment of some hyperbolic problems. Obviously, this point of view can be reversed:We hope that the topics of these notes will also capture the interest of some members of the elliptic community, willing to explore the links to the hyperbolic world
