Lectures on Gromov-Witten invariants of orbifolds

These are lecture notes of a C.I.M.E. course I gave at Cetraro, June 6-11 2005. The theory described is the version of Chen-Ruan's Gromov-Witten theory of orbifolds developed by Graber, Vistoli and me in the algebraic setting, but with introduction beginning in Kontsevich's formula on rational plane curves and through Gromov-Witten theory of algebraic manifolds. As this is not a joint paper, I finally get to give direct credit to Vistoli's beautiful ideas! In the appendix, I include, with permissions, two relevant letters Kontsevich wrote to Borisov in July 1996. People who study motivic integration might want to read and understand something they have found confounding.