The review analyzes the results of theoretical investigations of excitons states (electron - hole pairs states) in a quasi - zero - dimensional nanosystems consisting of spherical semiconductor nanocrystals (quantum dots) placed in transparent dielectric matrices. The theory of exciton states in a quantum dot under conditions of dominating polarization interaction of an electron and a hole with a spherical (quantum dot – dielectric matrix) interface are developed. An shown, that the energy spectrum of heavy hole in the valence band quantum dot is equivalent to the spectrum of hole carrying out oscillator vibrations in the adiabatic electron potential. In the framework of the dipole approximation theory are developed interband absorption of light in quasi – zero – dimensional nanosystems. An shown, that the absorption and emission edge of quantum dots is formed by two transitions of comparable intensity from different hole size – quantization levels and into a lower electron size – quantization level. Propose a theoretical prospect of using hole transitions between equidistant series of quantum levels observed in nanocrystals for desining a nanolaser. The theory of an exciton formed from spatially separated electron and hole (the hole is in the quantum dot volume, and the electron is localized at the outer spherical quantum dot–dielectric matrix interface) is developed within the modified effective mass method. The effect of significantly increasing the exciton binding energy in quantum dots of zinc selenide, synthesized in a borosilicate glass matrix, relative to that in a zinc selenide single crystal is revealed. We developed the theory of a biexcitons formed from spatially separated electrons and holes (the hole is in quantum dot volume, and the electron is localized at the outer surface of the quantum dot – dielectric matrix interface) in a nanosystem that consists of zinc selenide quantum dots synthesized in a glassy matrix.

The theoretical model of transmission spectrum of dielectric nanoparticles ensemble is presented. This model describes the dependence of the transmission spectrum on bot hof the particles size and the radiation frequency.This basis of the model is: the energy gap of the nanoparticle material contains energy levels, that is caused by the presence of a great number of defects of the nanoparticles crystal structure; the quantization of the charge carriers and excitons states. The theoretical model is compared with experimental results on the transmission spectrum.