ELFA (Electron Laser Facility for Acceleration) has both a fundamental and a technological novel goal: i) the fundamental goal is to test with short bunches the existence of three different high-gain regimes at the heart of FEL physics: the already observed steady-state regime and the two novel regimes of cooperative synchrotron radiation, i.e., weak and strong superradiance. ii) the technological goal consists in exploring the possibilities of matching the advanced technologies of high-gain FEL's and of superconductive acceleration. The experimental apparatus - photocathode injector, accelerating structure with 352 MHz superconducting cavities, wiggler - is discussed with emphasis on the problems related to the very high current, I ≈ 400 A. Alternative normal-conducting acceleration schemes at 1.3 GHz and 425 MHz are also discussed. The applications of ELFA should range from high-gradient particle acceleration to plasma heating and condensed matter physics.