The dissertation of V. M. Litvyak is devoted to the absorption spectroscopy of the lead chalcogenide quantum dots in glass matrixes. Narrow-bandgap PbS and PbSe based nanostructures are actively studied and they are promising materials for photovoltaic and optoelectronic applications. Further modernization of the optical devices requires solving of the fundamental tasks about the size-dependently quantized charge carrier spectrum of the quantum dots and about its optical transitions. The question about the nature of the inter-band optical transitions between the excited states of the PbS and PbSe quantum dots remains open and there is still a debate in the literature about it. The difficulty of this problem is coming from the complex band structure of the lead chalcogenides – these materials have many valleys and an anisotropic effective mass.   The understanding of the nature of the transitions requires the comparison of the results of theoretical calculations with the optical experiments. That is why the absorption spectroscopy of PbS quantum dots made in the work of V. M. Litvyak is relevant. A series of measurements of the absorption spectra on different samples with PbS quantum dots of different sizes in glass matrixes is performed in this work. The temperature dependence of the absorption is analyzed. Combination of low dispersion of quantum dots in diameter and high resolution of the original of the experimental setup allowed reliably follow the dimeter dependence not only of the first optical transition but also of three excited one.  Matching of the experimentally obtained absorption spectra with calculations decisively shows that the second and third transition are related to transitions between the excited p-type states of the electrons and holes split by the anisotropy of effective masses. Dissertation is performed on a high scientific level. The author demonstrates a deep understanding of the problem, a detailed analyzes of the current state of quantum dots physics, gives a detailed description of the peculiarities of the used experimental methods and different existing theoretical methods of calculations of optical spectra. The results presented clear. The work in written with the good language (from small defects not reducing a very good impression of work usage of the combination of words “Bohr exciton radius” instead of more often “exciton Bohr radius” or “Bohr radius of exciton”).      I believe that the work of Valentina Mikhailovna Litvyak meets all the necessary requirements for final qualification works. The dissertation deserves score “fine” and its author V.M. Litvyak – the award of master degree.