BESSY is planning to build a SASE FEL facility covering the photon energy range from 20 eV to 1 keV at the site next to the existing BESSY II storage ring. This new facility will offer laser like photon beams with fully coherent, high power (mJ) pulses of @<=@20 fs duration, enabling a whole set of novel experiments dedicated to understand dynamical processes in matter or for the investigations of very dilute systems. This SASE FEL covers the traditional BESSY II photon energy range, which is especially suited for electronic structure investigations of atoms, molecules, clusters, and solids. With the anticipated temporal resolution of @<=@20 fs charge transfer processes and time resolved 'femtochemistry' studies as well as magnetization dynamics in magnetic materials establish some of the major areas of scientific interest in this new facility. Furthermore in microscopy on soft-matter and biological samples it is possible to acquire an image using a single laser pulse. Thus stroboscopic time resolved images of dynamical processes in living cells become possible. In general, the science planned at this facility is complementary to the science envisioned for the planned TESLA X-FEL facility at DESY and Linac Coherent Light Source (LCLS) at Stanford. Following the presentation of the parameters and the layout of the proposed facility, the Scientific Case will be presented as it was developed by the prospective user community in the course of several scientific workshops and in discussions.