This thesis introduces geometric dynamic active contours in the context of visual tracking, augmenting geometric curve evolution with physically motivated dynamics. Adding additional state information to an evolving curve lifts the curve evolution problem to space dimensions larger than two and thus forbids the use of classical level set techniques. This thesis therefore develops and explores level set methods for problems of higher codimension, putting an emphasis on the vector distance function based approach. This formalism is very general, it is interesting in its own right and still a challenging topic. Two different implementations for geometric dynamic active contours are explored: the full level set approach as well as a simpler partial level set approach. The full level set approach results in full topological flexibility and can deal with curve intersections in the image plane. However, it is computationally expensive. On the other hand the partial level set approach gives up the topological flexibility (intersecting curves cannot be represented) for increased computational efficiency. Contours colliding with different dynamic information (e.g., objects crossing in the image plane) will be merged in the partial level set approach whereas they will correctly traverse each other in the full level set approach. Both implementations are illustrated on synthetic and real examples. Compared to the traditional static curve evolution case, fundamentally different evolution behaviors can be obtained by propagating additional information along with every point on a curve.