Abstract Model independent expressions for the level density of systems of non-interacting Fermions are given in a form that is suitable for treating degenerate systems. No formal distinction is made between discrete and continuous distribution of the single Fermion states. The explicit solution as well as approximate formulae in various limiting cases are given for the case when the single Fermion distribution can be analyzed in a power series or a Fourier series. As an application the effect of nuclear shell structure on the level density is estimated. Finally, the influence on the level density of an energy gap in the single Fermion spectrum is discussed. It is shown that the introduction of an energy gap can account for the observed difference in level density of nuclei with odd and even number of nucleons.