A theoretical investigation of the adsorption of Mn single atoms and dimers on the (111) surface of Cu, Ag, and Au, within the framework of the density functional theory, is presented. First, the bulk and the clean (111) surface electronic structures are calculated, with results that agree well with previous reports. To understand the adatom-substrate interaction, also the electronic characteristics of the free Mn dimer are determined. Then, the electronic structure of the Mn adatom, chemisorbed on four different surface geometries, is analyzed for the three noble metals. It is found that the most stable geometry, in all three cases, Cu, Ag, and Au, occurs when the Mn atom is chemisorbed on threefold coordinated sites. For the dimer, the lowest-energy configuration corresponds to the molecule lying parallel to the surface. In the three noble metals, the geometry corresponds to both atoms chemisorbed in threefold coordinated sites, but with different local symmetry. It is also found that the magnetic configuration with the lowest energy corresponds to the antiferromagnetic arrangement of Mn atoms, with individual magnetic moments close to 5 mu(B). The ferromagnetic and antiferromagnetic solutions, in the case of a Ag substrate, are close in energy. It is also found that in this case the Mn-2 molecule is chemisorbed with very similar energy on various geometries. To study the dynamical motion of the dimer components, we calculated the potential energy barriers for the Mn motion in the various surfaces. In contrast to Cu and Au, this leads to the conclusion that on Ag the Mn dimer moves relatively freely.