The atomic-scale spin structure of individual isolated Skyrmions in an ultrathin film is investigated in real space by spin-polarized scanning tunneling microscopy. Their axial symmetry as well as their unique rotational sense is revealed by using both out-of-plane and in-plane sensitive tips. The size and shape of Skyrmions change as a function of the magnetic field. An analytical expression for the description of Skyrmions is proposed and applied to connect the experimental data to the original theoretical model describing chiral Skyrmions. Thereby, the relevant material parameters responsible for Skyrmion formation can be obtained.