CARMENES, Calar Alto high-Resolution search for M dwarfs with Exo-earths with a Near-infrared Echelle Spectrograph, is a study for a next-generation instrument for the 3.5m Calar Alto Telescope to be designed, built, integrated, and operated by a consortium of nine German and Spanish institutions. Our main objective is finding habitable exoplanets around M dwarfs, which will be achieved by radial velocity measurements on the m/s level in the near-infrared, where low-mass stars emit the bulk of their radiation.