Using first-principles calculations, we present a comprehensive study on the atomic and electronic structures of metal adatoms (noble metals Ag, Au, Cu and alkali metals Li, Na, K) adsorbed on a [Formula: see text]-Ag (hereafter [Formula: see text]-Ag) surface. We found that adsorption of noble and alkali adatoms can induce significant structural changes in the topmost Ag layer. The most striking and interesting results are the immersion of the noble and Li adatoms into the substrate Ag layer and the finding of the most stable configurations with three adatoms incorporating into or being adsorbed on the surface dependent on their atomic radii. We also found that the almost empty two-dimensional free-electron-like band s1 and its band folding s1(*) of the original surface band s1 of the [Formula: see text]-Ag surface split into a gap at the surface Brillouin zone (SBZ) boundary with adsorption of an adatom. The two surface bands gradually move downwards and the s1 band is gradually filled with an increase of coverage. The s1 band is fully occupied with the largest band gap ∼ 0.25 eV between the s1 and s1(*) bands at the critical coverage of 0.14 monolayers (ML) [three adatoms in a [Formula: see text]-Ag (hereafter [Formula: see text]-Ag) unit cell], which corresponds to the most stable adsorption phase. Although the adsorption configurations are different, both the noble and alkali adatom adsorptions give rise to similar electronic structures at low coverages, indicating a free-electron-like character of the adsorption surfaces.