Abstarct: In this thesis, the structural, electronic, magnetic, and optical properties of double perovskites (A2MnB'O6) were investigated using density functional theory (DFT) with both GGA and GGA+U approaches implemented in SIESTA code. At the first step, Sr2MnVO6 (SMVO) compound as a half-mextallic (HM) double perovskite was predicted with the simultaneous presence of ferromagnetism and polar distortion. DFT calculated the structural, electronic, and magnetic properties of SMVO with GGA(+U) approximation. Different orderings of B and B′ cationic sites were evaluated, including rocksalt, columnar and laxyered arrangements for cubic, monoclinic, and tetragonal crystal structures. The calculations showed that the most stable ordering was obtained when Mn and V were placed in a laxyered type ordering a tetragonal crystal structure with an I4/m space group. The B-site ordering of the Mn3+ and V5+ ions in a laxyered configuration led to ferromagnetically coupled magnetic moments of 4.17 μB at the Mn site and 0.23 μB at the V site. The density of states calculations showed that SMVO is a half mextallic compound with a band gap of 0.65 eV for spin down channel. The off-centered displacement of V atoms in the octahedral cage can cause ferroelectricity. By applying UMn, V = 4 eV, the energy gap of the spin down channel and the local magnetic moment of Mn and V increased. Therefore, SMVO was predicted to be a polar HM material and a promising candidate for a multiferroic property with potential application in spintronics. In following, the structural, electronic and magnetic properties of electron-doped Sr2-xAxMnVO6 (A = Sn, Bi) for x = 0.5, 1.0, 1.5, 2.0 were investigated. A structural phase transition from tetragonal to monoclinic and triclinic structures was observed for different doped compounds. Calculations demonstrated a half mextal semiconductor transition for Sr2-xAxMnVO6 with x < 2.0 and x > 0.5 upon Sn and Bi doping, respectively. Ferromagnetic coupling between Mn and V was found to be the ground state for all doping concentrations of Sn and Bi. By substitution of Sr with Sn (Bi), the total magnetic moments increase to 15.73 (12.0) μB for x = 2.0. Calculated distortion parameters and bond angles indicated that the end members of each series, Sn2MnVO6 (SnMVO) and Bi2MnVO6 (BiMVO), undergo a significant octahedral tilting and distortion, which may result in a large value of electric polarization and hence, may be suggested as potential multiferroic materials. In the next step, to investigate the impact of different ions at B site, in SnMVO compound, we substituted Ta with V ion and studied the structural, electronic, and magnetic properties of double perovskite Sn2MnTaO6 (SnMTO). Structural calculations showed that triclinic crystal structure (space group P1) is the most stable structure of SnMTO. Electronic calculations with GGA(+U) method indicated that SnMTO is an antiferromagnetic semiconductor with a band gap of 1.05 (1.10) eV and 1.15 (1.20) eV for the spin up and down channels, respectively. Finally, to investigate the optical behaviour of studied double perovskites SMVO, SnMVO, BiMVO, and SnMTO, these compounds’ optical properties, including dielectric function and absorption coefficient, were calculated using GGA(+U). The calculations showed that in case of the SMVO and SnMVO, due to the mextallic behaviour of spin up channels, the absorption starts from small energy values. For BiMVO and SnMTO, the absorption edge starts from the energy of about 1 eV as it covers all the visible spectra; moreover, the value of the absorption coefficient in the energy range of 0-8 eV is in the order of 105 cm-1. These results indicated that BiMVO and SnMTO are promising candidates for photovoltaic applications.