The review article deals with ‘quantum engineering’ of growing of silver films on semiconductor substrates that allows obtaining new forms of matter. The results on the energy dispersion of electron states in epitaxial Ag(111) films obtained on Si(001) and Si(111) are presented. The splitting of bands is explained, and analysis of the Shockley’s surface states is given. Superstructures, which are formed on the surface of monolayer silver nanostructures, are analysed in detail. A detailed analysis of the energy states of the noble-metal quantum wells is given. The mechanism of formation of a noble-metal nanorelief on the (111) and (110) surfaces of Si single crystal during multistage thermal deposition is investigated. The symmetry of the interface surface of the single-crystal Si(111)7$\times$7 silicon plane is deterministic in the growth mechanism of the hexagonal-pyramidal structures of copper, silver, and gold. The morphological features of the indium surface during its thermal deposition on the Si(111) and Si(110) surfaces are investigated. The formation of clusters of a regular cubic shape is observed that indicates the formation of In nanocrystals. The formation of In nanoclusters (of $\approx$10 nm size) on the Si(111) surface and the subsequent modification of the single-crystal surface morphology response in the calculated curves of electron density of states.