Square-shaped thin film structures with a single magnetic vortex were investigated using a scanning transmission x-ray microscope. The authors report on the direct observation of the vortex core in 500x500 nm(2), 40 nm thick soft magnetic Ni-Fe samples. The static configuration of the vortex core was imaged as well as the gyrotropic motion of the core under excitation with an in-plane alternating magnetic field. This enabled them to directly visualize the direction of the out-of-plane magnetization in the vortex core (up or down). The reversal of the core was effected by short bursts of an alternating magnetic field. An asymmetry appears in the core's trajectory for its orientation pointing up and down, respectively.