The aim of the project was to develop strong permanent magnets using nanoparticles and their composites. For this an understanding of the magnetic properties of nanoparticles was also needed. Assemblies of nanoparticles can be used to develop novel exchange coupled strong magnets without using rare earths as well as for high density magnetic recording media. Some of these nanoparticles (such as Fe-Pt) can also be very interesting for catalysis. Fe-Pt is one of the most promising materials due to its large magnetic anisotropy. Ab initio calculations on Fe-Pt nanoalloys (clusters and nanoparticles) were performed to understand the atomic and electronic structure, and the magnetic behavior. The findings revealed a tendency for Pt segregation on the surface and a preference for maximizing Fe-Pt bonds. The formation energy of the nanoalloys is the highest around 50:50 composition as also in bulk Fe-Pt, but Pt tends to occupy low coordination sites. An icosahedral Fe72Pt75 (close to 50:50 composition) nanoparticle having 147 atoms ( 1.5 nm diameter) was investigated and found to phase separate into a Fe55 core and (Fe-Pt)92 ordered shell. These results show that such nanoparticles prefer decahedral or icosahedral structure and a transition to bulk structure should occur at significantly higher sizes, which agrees with experiments that show a transition to bulk structure in FePt nanoparticles for sizes larger than 2.5 nm. Further ab initio calculations were done for the first time on Fe3Pt type nanoparticles (soft magnetic material) embedded in FePt matrix (hard magnet) to model composites. These results revealed enhancement in the magnetic moments in both the nanoparticles and the matrix compared with the bulk behavior of the soft and hard phases and ferromagnetic coupling.