The potential applications of nanostructures and nanoparticles have attracted great attention in modern science and technology. Among these low dimensional systems, small atomic clusters of transition metal elements display interesting physical and chemical properties. Iron magnetic clusters are a group of transition metal clusters that because of their partially occupied d orbital, exhibit challenging physical behavior, from experimental as well as theoretical point of view. In this project, we study the physical properties of iron clusters in the framework of density functional theory by using the full potential numerical atom centered orbital technique implemented in FHI-aims omputational package. At the first stage, the accuracy parameters were optimized and the validity of the optimized results obtained by aims was verified by calculating and comparing the iron bulk properties within aims and wien2k codes. Then, after full relaxation of the atomic positions, the structural, electronic, magnetic and vibrational properties of Fe N (N=1-6) clusters were calculated. The results show that the ground state isomers are three dimensional and highly bonded structures with higher average atomic magnetic moment than the bulk value. In general, by increasing the number of cluster atoms, their various physical properties approach the bulk values. By applying the many body based GW correction, we obtained very good ionization potentials and electron affinities for Fe clusters, compared with the experimental data. In addition to the GW method, we also determined the ionization potentials and electron affinities by calculating the Kohn-Sham total energies of the natural and charged clusters. The observed agreement between these two approaches confirms validity of the total energies obtained by the Kohn-Sham scheme. In order to avoid agglomeration and oxidation of iron clusters in practical situations, usually they are coated by gold atoms. As a preliminary step toward understanding the effects of coating with gold, we studied the stability, magnetic properties, and the tendency to oxidation of the Fe clusters adsorbed by one Au atom. The results show that addition of one Au atom enhances stability of Fe clusters without considerable change of magnetic moments. Moreover, we observed that the Au head of the Fe N Au clusters does not prefer to adsorb an oxygen atom. This observation confirms the oxidation resistance of the Au coated Fe clusters. Keywords: Quantum computations, Density functional theory, Localized numeric atom-centered orbitals, FHI-aims software, Iron magnetic nanoparticles, GW many body correction, Gold atom adsorption, Oxygen atom adsorption.