Background.- The Quillen functors L and C, and their duals.- Complete differential graded Lie algebras.- Maurer-Cartan elements and the Deligne groupoid.- The Lawrence-Sullivan Interval.- The cosimplicial cdgl L.- The model and realization functors.- A model category for cdgl.- The cosimplicial cdgl L via transfer.- The Deligne-Getzler-Hinich functor MC and equivalence of realizations.- Examples.- Index of notation.