The magnetic coupling between single Co atoms adsorbed on a copper surface is determined by probing the Kondo resonance using low-temperature scanning tunneling microscopy. The Kondo resonance, which is due to magnetic correlation effects between the spin of a magnetic adatom and the conduction electrons of the substrate, is modified in a characteristic way by the coupling of the neighboring adatom spins. Increasing the interatomic distance of a cobalt dimer from 2.56 to 8.1 Å we follow the oscillatory transition from ferromagnetic to antiferromagnetic coupling. Adding a third atom to the antiferromagnetically coupled dimer results in the formation of a collective correlated state.