Operads, moduli space of Riemann surfaces and the Grothendieck-Teichmüller group

After recalling the relevant definitions, I will explain how one can view the Grothendieck-Teichmüller group as the group of automorphisms of the operad of moduli spaces of genus zero Riemann surfaces. If time permits, I will also explain a homotopical version of this result which is due to Pedro Boavida de Brito, Marcy Robertson and myself.