The Ph. D. thesis focuses on the solvothermal synthesis of degenerate Ga3+ doped ZnO semiconductor nanocrystals and the study of the crystalline structure, electronic structure and morphology, as well as optical and magnetic properties of the obtained materials. The experimental part investigates ways to achieve a higher degree of doping and the concentration of free charge carriers, as well as their effect on localized surface plasmon resonance-induced light absorption in the infrared part or the light spectrum or transition metals (Fe3+, Ni2+, Mn2+) doped ZnO magnetization nature. Literature review summarises information through the period from 1954 to 2020, using the latest literature, which is available on internet databases. The review provide information on various nanocrystal synthesis methods used to form zinc oxide nanocrystals. Degenerate semiconductor metal oxides, their optical properties, as well as diluted magnetic oxide semiconductor nanocrystals are considered as well. The results describes various doped ZnO nanocrystal products that are synthesis by the solvothermal synthesis method and their optical, morphological and physical properties. The results of the research show the possibility to adjust the amount of gallium introduced into ZnO nanocrystals by controlling solvents and additives. The magnetic properties of ZnO nanocrystals co-doped with transition metals and gallium change depending on the amount of gallium introduced, as well as by photodoping Ga-doped ZnO nanocrystals, it is possible to change the concentration of their free charge carriers. The dissertation is written in Latvian, consists of 111 pages, 83 pictures, 20 tables and 21 formulas, there are 160 cited literature sources.