Density functional theory (DFT) calculations have been performed to study the adsorpton of di-, tri-, and polyatomic gases on the anatase (001) and (101), rutile 001) and (110) surfaces of TiO₂-. The calculations empolying model clusters and periodic boundary conditions to detailed study the adsorption energies and adsorption geometries. It was foun that the most remarkable geommetry corresponds to the adsorption of gases diretly onto the Ti₅C site of these surfaces. The interaction between adsorbate and substrate for the anatase surface resulted weaker than that for the rutile. The hole-assisted conversion of CO to CO₂, the adsorption and conversion of N2O to N₂ on anatase TiO₂ (101) surface have been studies using first-principles calculations. The presence of the positive charge on the anatase (101) surface increases the adsorption energy of CO, allowing the it conversion of CO to CO₂ and leaving an oxygen vacancy behind. CO is found to be a good reducing agent for N₂O, in which CO is oxidized to CO₂ and N₂O is reduced to N₂ under photo-excitaton. Therefore, the results indicate that the oxidation of CO and the reduction of N₂O on the anatase (101) surface could be an efficient photocatalytic process. The investigation was extended to study the role of TiO₂-supported Pt of the anatase (101) surface (Pt/TiO₂) on the adsorption of CO, N₂, CO₂ and N₂O. It was found that the strong interaction between Pt atom and anatase (101) surface could be responsible for the enhanced adsorption of CO and CO₂.