LUSIFER: a LUcid approach to SIx-FERmion production. LUSIFER is a Monte Carlo event generator for all processes e+e-->6fermions, which is based on the multi-channel Monte Carlo integration technique and employs the full set of tree-level diagrams. External fermions are taken to be massless, but can be arbitrarily polarized. The calculation of the helicity amplitudes and of the squared matrix elements is presented in a compact way. Initial-state radiation is included at the leading logarithmic level using the structure-function approach. The discussion of numerical results contains a comprehensive list of cross sections relevant for a 500GeV collider, including a tuned comparison to results obtained with the combination of the WHIZARD and MADGRAPH packages as far as possible. Moreover, for off-shell top-quark pair production and the production of a Higgs boson in the intermediate mass range we additionally discuss some phenomenologically interesting distributions. Finally, we numerically analyze the effects of gauge-invariance violation by comparing various ways of introducing decay widths of intermediate top quarks, gauge and Higgs bosons.