This thesis investigates a novel class of magnetic phenomena in atomic- and nanoscale systems influenced by the interplay between exchange and relativistic spin-orbit interactions. It focuses on unique spin-textures with one- and two-dimensional periodicity observed in ultra-thin magnetic films on nonmagnetic metallic substrates with significant spin-orbit interaction. The research aims to extend the study to finite-sized magnetic clusters and nano-structures, exploring how cluster size and edge atoms, particularly sensitive to relativistic effects, alter the balance between interactions and lead to new magnetic behaviors. A detailed examination of Fe nano-islands on Ir(111) is included, highlighting the observation of a magnetic nanoskyrmion lattice in an Fe monolayer. To facilitate this research, a new first-principles all-electron electronic structure code based on density functional theory has been developed, utilizing the Korringa-Kohn-Rostoker (KKR) impurity Green function method. This approach advances the treatment of non-collinear magnetism and spin-orbit interaction without shape approximations, incorporating structural relaxation and embedding finite-sized magnetic clusters into surfaces or bulk materials. The formalism employs a Green function expansion with left- and right-hand side scattering solutions. Relativistic effects are addressed through the scalar-relativistic approximation and self-consistent spin-orbit
