The phenomenon of charge density waves (CDWs) is traditionally related to so called quasi-one-dimensional materials with a highly anisotropic Fermi surface that satisfies the nesting condition which brings about the possibility of Peierls instability. However, the realization of density waves in materials with closed Fermi surfaces which don’t satisfy the nesting condition, requires a qualitatively different mechanism of CDW stabilization. Such a mechanism was proposed by Kadigrobov et al. [Kadigrobov et al. Phys. Rev. B (2018)] for a case of 2D isotropic parabolic band and it is based on topological reconstruction of electron band subjected to a periodic potential causing a topological transformation of initially closed Fermi surface to an open one. The subject of this master’s thesis is the generalization of the proposed mechanism to the case of three-dimensional free-electron band and the investigation of the effect of anisotropy on the possibility of CDW stabilization. After a short introduction to the phenomenon of charge density waves in quasi-one-dimensional materials and the mechanism of their stabilization, namely Peierls instability, we give first a qualitative sketch of the mechanism of topological reconstruction and then calculate the effect of CDW ordering on electron dispersion of a three-dimensional free electron band using the mean field approximation. After that, we calculate the density of states (DOS) both for the case of two- and three-dimensional bands where anisotropy is introduced by varying the effective mass corresponding to a chosen direction in the original dispersion. We find that such a method of introducing anisotropy doesn’t bring about any qualitative change in the calculated density of states and, therefore, makes it impossible to connect our results for a 3D band with the results for a 2D band. For this reason, we turn to a new way of treating an anisotropic system as an isotropic system living in a space of non-integer dimensionality which seems nonsensical from a purely geometrical point of view, but makes sense from a physical one. Such a treatment enables us to obtain a smooth crossover of density of states as we vary the dimension in the range d ϵ [2, 3]. After that, we turn our attention to the ”energetics” of the system. As a preliminary result we establish, using the method of Lagrange multipliers, that the decrease of band energy due to band reconstruction is maximal (subject to the constraint of electron number conservation) when the Fermi energy remains as it was before the reconstruction. This result is general in so far as it does not depend on the details of the change in the density of states and it points to the fact that the energy decrease will be solely the effect of redistribution of filled states from higher toward lower energies caused by the change in DOS. Plugging this result back in the equation expressing electron number conservation enables us to find the optimal CDW wave vector of the CDW order parameter which differs more and more significantly from the value 2k_F0 required by Peierls instability as the dimension gets higher, where k_F0 is a Fermi wave number of the initial band. Using the optimal wave vector we calculate the relative decrease of band energy ΔE/E_0 which, when combined with the mean field phonon contribution (elastic energy of static lattice deformation), enables us to find that CDW stabilization via topological reconstruction is possible for all dimensions in range d ϵ [2, 3] if the dimensionless electron-phonon coupling constant λ is larger than its critical value λ_c which increases with dimension. In that sense, we conclude that CDW ordering is a quantum phase transition with respect to a parameter λ that determines the relative strength of electron-phonon interaction.