Self consistent, spin-polarized calculations are performed for Sc[subscript]2CuO[subscript]4, La[subscript]2CuO[subscript]4 with constrained d[superscript]9 configuration, and La[subscript]2NiO[subscript]4. For Sc[subscript]2CuO[subscript]4, both ferromagnetic and antiferromagnetic ground states are investigated and found to be unstable. Magnetic form factors are calculated and are discussed in view of experiments in La[subscript]2CuO[subscript]4. In the calculation for La[subscript]2CuO[subscript]4, the d[superscript]9 configuration is maintained by constraining the d[subscript]x[superscript]2-y[superscript]2 orbital to have exactly one hole. The Cu projected 3d density of states is compared with XPS data which show the binding energy of the Cu states is lower than the results from standard band structure calculations. The Cu d states are treated as core states and no hybridization is considered. This results in the d density of states being too narrow compared with experiment and the difference indicates the degree of hybridization with the oxygen 2p states. For La[subscript]2NiO[subscript]4, only the antiferromagnetic ground state is investigated and found to be stable but with the local moment on Ni being too small compared with experiment. The magnetic form factor for the antiferromagnetic state is examined and discussed in view of experiments. All these results indicate the local spin density functional approximation (LSDA) does not give correct solutions for these materials;To go beyond the LSDA, we study the extended Hubbard model. A mean field calculation of the two dimensional one and three band Hubbard models based on a Mori-projection operator formalism, which is called the projection operator mean field (POMF) approximation, is presented. The results are compared with those of the Hartree-Fork (HF) approximation, the Hubbard I approximation, and Quantum Monte Carlo (QMC) simulations. We find that the POMF results agree very well with those of the QMC. Then we use the parameters determined by the constrained density functional method to study the CuO[subscript]2 plane by POMF. We find an antiferromagnetic insulating ground state with band gap and magnetic moment given by 1.97eV and 0.65[nu][subscript]B, and a satellite peak around 13eV below Fermi level. All these results agree with experiment. The effect of doping on the solutions is discussed. Finally, we study CuO[subscript]2 with various sets of parameters to examine the effect on the solution of each parameter.