In this thesis we investigated the electronic and magnetic properties of Tb 2 Ti 2 O 7 , which is a frustrated cubic pyrochlore oxide with spin liquid phase. We used Density Functional Theory (DFT) to explore the electronic and magnetic properties of this system. All DFT calculations have been done with FP-LAPW method by use of Fleur code. We approached exchange-correlation energy of electrons with GGA and GGA+U functionals. The GGA calculations predict a magnetic metallic state for Tb 2 Ti 2 O 7 which is in conflict with the experiment. Using GGA+U, we could correct coulomb interactions between f electrons therefore Tb 2 Ti 2 O 7 is converted to a magnetic insulator. The analysis of electronic density of state (DOS) shows 4f electrons of Tb atoms as the source of magnetism. This analysis also indicates a weak hybridization between Tb f orbitals and O ? p orbitals. Because of existence of strong spin-orbit coupling (SOC) in f electrons we repeated the calculations with GGA+U+SOC for noncollinear configurations in addition to the collinear ones. The magnetic moment of Tb obtained 7 .3 and 7 .1 from collinear and noncollinear calculations, respectively. But in the experiment the magnetic moment of Tb was measured about 5 . In fact the DFT calculations are trapped in the local minima and in order to improve the magnetic moment of Tb we need a more sophisticated methods to find the global minimum in our electronic structure calculations. To investigate the ground state of Tb 2 Ti 2 O 7 , we compared total energies in two configurations, all-in (long-rang order) and two-in/two-out (spin-ice order). We found that the all-in is more stable than two-in/two-out.