This report describes the accelerator physics aspects, the engineering considerations and the choice of parameters that led to the accelerator design of the FERMI Free-Electron-Laser. The accelerator (also called the "electron beam delivery system") covers the region from the exit of the injector to the entrance of the first FEL undulator. The considerations that led to the proposed configuration were made on the basis of a study that explored various options and performance limits. This work follows previous studies of x-ray FEL facilities (SLAC LCLS [1], DESY XFEL [2], PAL XFEL [3], MIT [4], BESSY FEL[5], LBNL LUX [6], Daresbury 4GLS [7]) and integrates many of the ideas that were developed there. Several issues specific to harmonic cascade FELs, and that had not yet been comprehensively studied, were also encountered and tackled. A particularly difficult issue was the need to meet the requirement for high peak current and small slice energy spread, as the specification for the ratio of these two parameters (that defines the peak brightness of the electron beam) is almost a factor of two higher than that of the LCLS's SASE FEL. Another challenging aspect was the demand to produce an electron beam with as uniform as possible peak current and energy distributions along the bunch, a condition that was met by introducing novel beam dynamics techniques. Part of the challenge was due to the fact that there were no readily available computational tools to carry out reliable calculations, and these had to be developed. Most of the information reported in this study is available in the form of scientific publications, and is partly reproduced here for the convenience of the reader.