The paper introduces a novel method for computing transition pathways, free energy barriers, and transition rates in complex systems with smooth energy landscapes. The method involves evolving strings, which are smooth curves with intrinsic parametrization, to find the most probable transition paths between metastable states. The strings satisfy a differential equation that ensures they evolve along the most likely transition paths. Free energy barriers and transition rates can be determined through umbrella sampling around the strings. The authors demonstrate the method's effectiveness in two applications: Lennard-Jones cluster rearrangement and thermally induced switching of a magnetic film. The intrinsic parametrization of the strings simplifies the numerical solution of the evolution equation and allows for efficient sampling of configuration space. The method is compared to the nudged elastic band (NEB) method, showing advantages in flexibility and efficiency.The paper introduces a novel method for computing transition pathways, free energy barriers, and transition rates in complex systems with smooth energy landscapes. The method involves evolving strings, which are smooth curves with intrinsic parametrization, to find the most probable transition paths between metastable states. The strings satisfy a differential equation that ensures they evolve along the most likely transition paths. Free energy barriers and transition rates can be determined through umbrella sampling around the strings. The authors demonstrate the method's effectiveness in two applications: Lennard-Jones cluster rearrangement and thermally induced switching of a magnetic film. The intrinsic parametrization of the strings simplifies the numerical solution of the evolution equation and allows for efficient sampling of configuration space. The method is compared to the nudged elastic band (NEB) method, showing advantages in flexibility and efficiency.