In this thesis, we first investigate the physical properties of some metal atoms, molecules and their clusters. We then study the interaction of these with silicon and graphene surfaces. The adsorption of NH3 and H2S molecules on Au3Pt3 is also studied. We calculate the equilibrium atomic structures of metal clusters using density functional theory (DFT) up to eight atoms. The electronic structures of these free and adsorbed clusters are also calculated in detail. We find that the adsorption generally modifies the structure of the Au3Pt3 cluster and the adsorbate (NH3 and H2S ). We also study the site-dependent shapes of the Au8 cluster, associated adsorption energies, band structures and the corresponding charge distribution for the S i(100) asymmetric surface. We show that the electronic properties of the cluster and the substrate complex change with the location of the cluster on the surface. We study the AunPtn clusters on graphene surface. We observe that graphene can be metallic or semiconducting depending on the number of Au and Pt atoms in the cluster and the charge transfer between the cluster and the graphene. We have studied bismuth both as an adsorbate and substitutional dopant in graphene. We have shown that bismuth causes a weak p-type doping for the adsorption case within generalized gradient approximation (GGA), but it n-dopes graphene when it is substitutional and for the adsorption case within local density approximation (LDA). Our results are in agreement with recent angle-resolved photoemission results for the weak adsorption.