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This is the first project  report for ECE 5390/MSE 5472, focusing on the models and analyzing the conductance of 1D charge density waves (CDW). For normal conductors, the charge density in the conducting band is uniform (Fig.1(a)) but for certain materials, the charge density fluctuates with position. The CDW is the ground state of many quasi-1D materials, such as NbSe$_3$ when cooled down below Peierls temperature $T_P$ and undergoing Peierls Transition \cite{Peierls_1956}. Below $T_P$, the distortion of lattice minimizes the total energy of conducting electrons and the elastic energy of the distortion, rendering it the energetically favorable state. The electrons pile up around the periodic distortion potentials and the charge density in the conducting band varies with the same period $2k_F$ (Fig.1(b)).