This thesis reports results on magnetic properties of supported cobalt nanostructures. The nanostructures were grown on single crystal metal surface by Molecular Beam Epitaxy in an Ultra High Vacuum chamber. Our experimental setup is based on two in situ measurement techniques. The first is the Scanning Tunneling Microscope (STM) allowing to investigate the nanostructure morphology. The second, called Surface Magneto-Optical Kerr Effect (SMOKE), probes the magnetism of the nanostructures. By combining the data obtained with both techniques we were able to investigate the magnetism of 2D nanoparticles down to the atomic level. The first aim of the thesis consisted in disclosing the role played by the differently coordinated atoms in determining the Magnetic Energy Anisotropy in 2D nanostructures. To this purpose, we performed experiments on the Co/Pt(111) system, chosen as a model system since the Pt surface is well known to increase the out-of-plane uniaxial anisotropy as well as the magnetic moment of the Co islands. A preliminary work has been devoted to the growth of the Co islands as a function of the deposition and annealing temperatures. As a result, we learned to grow three different island's shapes : ramified, compact and double-layer islands. We then concentrated on the magnetism of these islands. Due to the nonlinear relationship between perimeter length and surface area, we were able to distinguish the different contributions to the anisotropy energy of surface and perimeter atoms. We found that the magnetic anisotropy in 2D Co nanostructures is predominantly due to the low-coordinated edge atoms, for which the anisotropy energy can be as large as 20 times the bulk value. This finding opens new possibilities to separately tune the anisotropy and moment of nanostructures. To exemplify this, and to illustrate once more the role of perimeter atoms, we produced Co island with a non-magnetic Pt core. As expected, these bimetallic islands have identical anisotropy and lower magnetic moment to their equally shaped pure Co counterpart. The second aim we focused on was the investigation of the magnetic properties of ultra-high density arrays of nanostructures created by self-assembly. We chose Co/Au(788) as a model system since the nanoscopic Co dots were found to have a very narrow size distribution and to be placed onto a lattice which is phase coherent on a macroscopic length scale. Moreover, the array has a density of 26 Tdot/in2 which allows the investigation of inter-particle interaction in ultra high density arrays. We showed that the narrow size distribution of the dots corresponds to an unprecedented narrow Magnetic Anisotropy Energy distribution with 35% width at half of the maximum. Moreover, we demonstrated the weak magnetic coupling between the Co dots despite their high density. In parallel to these fundamental researches, we developed a new experimental setup that will replace the current one. We designed a UHV chamber equipped with a homemade variable temperature STM combined with a SMOKE experiment. A quadrupole, focused on the sample, generates a 0.35 T magnetic field. This field is one order of magnitude larger than the present one and can be uniformly rotated in the plane of the quadrupole. Furthermore, the design of the new chamber allows STM imaging in this magnetic field. In this report, we present the adopted solutions as well as the first tests of the components (STM, SMOKE, cryostat).