Operads and -spaces.- Operads and monads.- A? and E? operads.- The little cubes operads .- Iterated loop spaces and the .- The approximation theorem.- Cofibrations and quasi-fibrations.- The smash and composition products.- A categorical construction.- Monoidal categories.- Geometric realization of simplicial spaces.- Geometric realization and S*, C*, and ?*.- The recognition principle and A? spaces.- E? spaces and infinite loop sequences.- Remarks concerning the recognition principle.