Quasi two dimensional structures are among the most interesting structures in the study of high T c superconductors. In strongly correlated electron systems, superconductivity is usually accompanied by magnetic or charge ordering. Transition metal dichalcogenide compounds are consisted of layered structure which undergo to charge density waves by decreasing temperature. e 2 is one of these compounds which shows charge density waves and superconductivity below 33.5K and 7.2K, respectively; These two phases coexist at lower temperatures. Unlike the other charge density wave conductors, e 2 becomes a better conductor within the transition to charge density waves. There are many attempts to find the mechanism of charge density waves in these materials. Two main mechanisms have proposed for it: (a) nesting in Fermi surfaces, (b) saddle point. In this thesis at first the interplay between antiferromagnetism and d-wave superconductivity is studied.Besides the condition of appearance of the spin triplet amplitude and its robustness in square lattice are evaluated. The dynamical generation of the new order parameter is not restricted to a system with antiferromagnetism and d-wave superconductor but is a generic feature for fermionic systems. The antiferromagnetism and superconductivity occur in strongly correlated electron systems. Therefore, we use the extended Hubbard model for these systems. In spite of the simplicity of this Hamiltonian its exact study is complicated and even impossible. Therefore, for its solution several approximations are used. One of these approximations is the mean field theory. To study the ordered phases, in finite temperatures, it is necessary to calculate free energy in the mean field approximation and to use optimization procedure. Therefore, a self consistent equation is obtained for each order parameter. By numerical solution of these equations, the order parameters are obtained in various temperatures and doppings. Then one can draw the phase diagrams of the system. In the following section, to study the charge density waves for the family of e 2 materials, for simplicity we consider the lattice as a triangular lattice with three atom basis. But the calculation of its Hamiltonian is complicated too. Therefore we reduce our calculations to the triangular lattice with one atom basis. Then we calculate the ground state energy and optimize it to find out the order parameters and draw the ground state energy versus order parameters for which we can determine the ground state phase and the behavior of the system at zero temperature. Finally we study the antiferromagnetism and charge density waves in the honeycomb lattice and the interplay between them. In this case, we will draw the order parameter versus on-site and off-site amplitudes of coulomb interaction. We will calculate the critical amplitude. Therefore we will be able to explain the behavior of the honeycomb lattice in zero temperature. Keywords: Extended Hubbard model, Mean field theory, Transition metal dichalcogenide, e 2 , Honeycomb lattice, Charge density waves, Antiferromagnetism, Superconductivity, ? triplet.