Photoemission experiments have been performed to investigate the electronic structure of Cu adlayers on a Pt(111) surface. The evolution of the $3d$ states as a function of Cu coverage is observed at the Cooper minimum of the $\mathrm{Pt}5d$ emission ($h\ensuremath{\nu}=150$ eV), where the $\mathrm{Cu}3d$ emission is enhanced. For Cu coverages up to \ensuremath{\sim}0.6 of the first monolayer (ML), the $3d$ states give a symmetrical and resonancelike peak with a maximum at -2.6 to -2.7 eV with respect to the Fermi level ${E}_{F}$, and a full width at half maximum of 1.4 to 0.5 eV. Between \ensuremath{\sim}0.6 and \ensuremath{\sim}1 ML, there is an increase in $\mathrm{Cu}3d$ emission around -3.5 eV, suggesting the onset of two-dimensional delocalization. The delocalization of the $3d$ states increases with increasing Cu coverage. Beyond \ensuremath{\sim}1 ML, Cu-Cu bonding states appear below -4 eV as well. The Cu adlayers studied, from submonolayer coverages up to \ensuremath{\sim}1.5 ML, show an interesting absence of Cu-derived emission near ${E}_{F}$, in contrast with the flat emission at the corresponding energies shown by pure Cu. For small (\ensuremath{\le}0.6 ML) submonolayer coverage, the $\mathrm{Cu}2{p}_{\frac{3}{2}}$ core level, excited by $\mathrm{Mg}K\ensuremath{\alpha}$ radiation, is observed to be shifted (upward) by -0.60 to -0.65 eV relative to the bulk $\mathrm{Cu}2{p}_{\frac{3}{2}}$ core level. By 3 ML, the $\mathrm{Cu}2{p}_{\frac{3}{2}}$ binding energy is almost identical with that of a pure Cu sample. The adsorption of Cu removes the $\mathrm{Pt}4{f}_{\frac{7}{2}}$ surface core level, which then becomes bulklike. The adsorption of Cu also results in a work-function decrease. However, the $\mathrm{Pt}4{f}_{\frac{7}{2}}$ core-level data do not permit the work-function decrease to be explained by simplistic arguments based on charge transfer.