We present the first experimental realization and characterization of two-dimensional Skyrmions and half-Skyrmions in a spin-2 Bose-Einstein condensate. The continuous rotation of the local spin of the Skyrmion through an angle of pi (and half-Skyrmion through an angle of pi/2) across the cloud is confirmed by the spatial distribution of the three spin states as parametrized by the bending angle of the l vector. The winding number w = (0,1,2) of the internal spin states comprising the Skyrmions is confirmed through matter-wave interference.