The total and partial densities of electron states of layered gold structures of different symmetry with thickness from 1 to 10 monolayers are calculated within the framework of the density functional theory. As shown, the first co-ordination sphere is determinant in the formation of the fine structure and the extent of the valence bands of the monolayer gold structures. The splitting of the peaks of the TDOS curve, which leads to its finer structure, is influenced not only by the lengths of interatomic bonds, but by the mutual arrangement of atoms too. The influence of long-range interactions on the electronic structure of gold monolayers is established. For example, for the (110) plane, a change in the atomic ordering in the third co-ordination sphere as a result of the introduction of a vacancy leads to noticeable changes in the TDOS curve that indicates either a significant role of the atoms of the third co-ordination sphere, or a significant redistribution of the interaction of $d$-orbitals of different symmetries of close neighbours. A correlation between the packing density as well as the number of neighbours in the first co-ordination sphere and the width of the energy bands of gold monolayers is revealed.