The dissertation investigates the statistical and thermal properties of mesoscopic systems and applies it to the multi-nucleon systems. The investigation was carried out using four approaches starting from the simplest and progressing to the more sophisticated. The first approach develops and employs the three-dimensional simple harmonic oscillator (3D-SHO) quantum statistics to obtain the thermal properties of multi-particle systems. The recently discovered method that relates the single particle oscillator properties to the multi particle oscillator is applied. The approach is successful in predicting observables at temperatures beginning slightly above the ground state domain for nuclear systems. The 3D-SHO potential function is spherically symmetric because the value of the potential depends only on distance. Because of this high degree of symmetry, the states of the three-dimension SHO are highly degenerate. Accordingly, the 3D-SHO approach has a limited capability to address the intrashell excitations, which significantly limits the utility of the predicted level density of the system, especially at low excitation energies. To account more completely for the intrashell effect, a second approach is introduced. In this approach, the single particle states of a temperature-independent mean field Hamiltonian are generated. Those states are used as an input to generate thermally populated states of the desired multi-fermion system. The thermal population procedures are similar to those used with the single particle 3D-SHO. The approach involves an un-physical condensation of the fermions at the very low temperature range. Above this un-physical condensation region, however, the approach gives a good description for the nuclear level densities. Due to computational obstacles, the range of unphysical condensation temperature is undetermined for nuclei with mass number larger than 24 and this limits the application of the mean-field approach at the present time. In attempting to improve the fundamental concepts of the quantum statistics, Tsallis' description for statistical mechanics, which introduces a new parameter, is investigated in some detail. We advance this theory by introducing the generalized-thermodynamic relations and expand the applications of the theory to include many fermion systems for a certain range of the new parameter in this approach. The additional parameter introduced by Tsallis suppresses the thermal response of the system at a given temperature. Ultimately, theory must derive this parameter from the Hamiltonian dynamics in order for the theory to have true predictive power. The last investigation employs the moment method to predict the nuclear level density from the Hamiltonian. This involves extracting the central moment of a fully microscopic no-core shell model Hamiltonian and using the Gram-Charlier expansion function to represent the level density of the system. The key advantage is that one can compute these moments without having to compute the full many-body spectra. The results are encouraging and imply that the no-core shell model can be used to predict nuclear level densities for heavy nuclei in larger model spaces, i.e. for situations beyond the conventional direct diagonalization techniques. A further improvement to the moment method using configuration moments approach is also investigated.