The experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. In this thesis, first an overview of theoretical and experimental facts on ultra-cold atomic gases is presented. Then a Green’s function scheme to study coherent transport by fermions through a one-dimensional array of potential wells is described. Within this scheme different geometries for the array like single-period, double-period and Fibonacci-ordered quasi-periodic array are considered. In conclusion, a novel spin-densityfunctional approach is introduced to study the ground-state of a one-dimensional trapped Fermi gases inside one-dimensional optical lattices. This approach enables the author to investigate both repulsive and attractive Fermi gases within a localspin-density approximation. Different phases caused by a spin-dependent trap for repulsive gas and also by a spin-imbalanced population for attractive gas are analyzed.