The aim of this project is to investigate the formation, dynamics, and thermal stability of magnetic vortices and related topological spin textures in low-dimensional magnetic systems. Magnetic vortices and antivortices play an important role in the finite-temperature behavior of two-dimensional magnets and are closely connected to vortex-mediated phase transitions, magnetic fluctuations, and the dynamical response of spin systems. We will use atomistic spin-dynamics simulations to study how vortices are created, evolve, interact, and annihilate as a function of temperature, system size, and microscopic magnetic interactions. Particular attention will be given to the role of exchange interactions and magnetic anisotropy in controlling vortex stability and proliferation. The project will also investigate the time stability and lifetime of individual vortex configurations. By following the magnetic configuration over extended simulation times, we aim to determine under which conditions vortices remain stable, move through the system, annihilate with antivortices, or are generated by thermal fluctuations. Temperature-dependent simulations will be used to connect vortex behavior with thermodynamic properties of the magnetic system. Quantities such as magnetization, susceptibility, heat capacity, vortex density, and Binder cumulants will be analyzed in order to characterize magnetic phase transitions and finite-size effects. Simulations for several system sizes and independent stochastic realizations will allow statistically reliable conclusions to be obtained. The calculations will be performed using the UppASD atomistic spin-dynamics framework. The overall goal is to obtain a microscopic understanding of thermally driven vortex phenomena and their relation to magnetic phase transitions in low-dimensional materials. The results are expected to contribute to the broader understanding of topological magnetic excitations and finite-temperature magnetism, with potential relevance for future spintronic applications.