This book is based upon a set lecture notes for a course that I was teaching at the University of Utah in Fall of 2002. Our main goal is to describe various tools of quasi-isometric rigidity and to give (essentially self-contained) proofs of several fundamental theorems in this area: Gromov's theorem on groups of polynomial growth and Schwartz's quasi-isometric rigidity theorem for nonuniform lattices in the realhyperbolic spaces. We conclude with a survey of the quasi-isometric rigidity theory.