Silver is the metallic elements, and it has been employed most extensively since ancient times to fight infections and control spoilage. Recently, nanotechnology is employed to increases surface to volume ratio and consequently, increases surface to volume ratio so it will increase the effectiveness and reactivity of matters, by producing nanoparticles. Silver nanocluster are ideal candidates for catalysis and antibacterial applications. Alloying silver with other metals such as palladium will help to increase catalytic properties. In this thesis, we applied the computer program package " Fritz Haber Institute ab initio molecular simulations (FHI-aims) '' , to study structural, electronic, magnetic and vibrational properties of pure silver nanoclusters and silver-palladium alloy (Ag _n-1 Pd and Ag n-2 Pd 2 ) nanoclusters. This computational package is primarily based on the density functional theory , although some many-body corrections such as GW self-energy are also involved. In order to verify the the accuracy of the FHI-aims calculations, structural and electronic properties of dimer and crystal of silver has been reinvestigated by using the computational package WIEN2k. We observed good agreement between the results of two packages. After optimization of input parameters and selection of appropriate exchange-correlation functional, the Two to nine atomic silver clusters investigated and for each cluster more stable structures are determined . The Jahn–Teller effect is observed in structural relaxation of high symmetry structures. Next, the average coordination number and bond length, d issociation energy and electron affinity energy, ionization potential, HOMO-LUMO energy gap, magnetic moment and vibrational properties of the most stable clusters were calculated. Finally, the general trend of the effect size on these properties were investigated. Calculations show that up to size of 6 (heptamer), silver clusters prefer two dimensional (2D) planar structures while larger clusters stabilize in 3D geometries. we observed that by increasing the cluster size, both average coordination number and bond length quantities as well as binding energy smoothly approach the corresponding bulk values. Presence of a pair electron in HOMO level of silver clusters with even number of atoms makes these systems non- magnetic and also more stable than odd clusters. The calculated binding energies and second order energy differences confirm 2 and 8 as the magic numbers of pure silver clusters, in agreement with experiment. After determining the most stable structures of clusters of silver-palladium alloys, it was seen that in the Clusters of silver alloy with one palladium atom (Ag _n-1 Pd ), structural transition from two dimension to three dimension occurs at the seven atoms cluster, similar to the pure silver clusters. Moreover, stable atomic configurations of the the allay clusters having less than seven atoms are similar to the corresponding to the pure silver clusters. On the other hand, the most stable structure of alloy clusters with two palladium atoms ( Ag n-2 Pd 2 ) at least four atoms, are three dimensional structure. Comparing with the literature data, we observed that atomic configuration Ag n-2 Pd 2 clusters are similar to the corresponding pure palladium clusters. our calculations show that the relative stability and consequently magic numbers of silver-palladium alloy clusters, compared with the pure silver clusters, has changed. Keywords: D ensity functional theory , FHI- aims, Ag cluster , AgPd cluster , M agic number, GW correction