Matterwave interferometers exploit the fact that atoms can behave just like waves, which can be sent along two different paths and can be brought to interfere. One can use this to measure minuscule energy differences between the two paths. These can be caused by anything that interacts with the atoms, but chiefly acceleration forces. Examples for this include Sagnac interferometers for rotation or Michelson interferometers for earthβs acceleration. The superb control afforded for neutral atoms places these sensors amongst the most sensitive detectors known today, which might be able to detect even Gravitational Waves in the not so distant future.In this talk, I will first present the general principles of matter-wave interferometry and some of its simpler applications. I will then introduce ELGAR (the European Laboratory for Gravitation and Atom-interferometric Research), which we proposed last year. The main aim of ELGAR is the detection of gravitational waves in a frequency range of a few Hz, which lies between LISA and LIGO /VIRGO. It would consist of many tens of matterwave interferometers spaced over 10 km and connected via a large optical resonator. This would allow us not only to measure the direction of the origin of a gravitational disturbance but also its wave-front curvature β and thus distinguish between local and distant objects.