We grow epitaxial graphene monolayers on Ru(0001) that cover uniformly the substrate over lateral distances larger than several microns. The weakly coupled graphene monolayer is periodically rippled and it shows charge inhomogeneities in the charge distribution. Real space measurements by scanning tunneling spectroscopy reveal the existence of electron pockets at the higher parts of the ripples, as predicted by a simple theoretical model. We also visualize the geometric and electronic structure of edges of graphene nanoislands.