Determining the quantitative and qualitative composition of solutes is an important scientific and applied problem that arises in various fields of science and technology. However, in a number of practical problems there is a need to determine the concentration of substances whose mass (volume) fraction in the solution is quite small. Common measurement methods, characterized by high speed and versatility are refractometric methods. Of particular interest among refractometric methods in the measurement of low concentrations of solutes is the method based on the use of the effect of surface plasmon resonance. The main advantages of this method are its high sensitivity and low weight of the sample used in the study. To date, the widespread use of this method of measurement is significantly limited by the lack of high-precision mathematical models of primary measuring transducers (sensors) implemented on its basis. The main directions of refractometry development and its relevance in various spheres of human activity, such as science, technology, medicine and even the food industry, were considered in the work. As a result of the need to use the phenomenon of surface-plasmon effect, a detailed description of this phenomenon, its features, nature and practical application. The peculiarity of the interaction of radiation with gold nanofilms is considered. A mathematical model of the refractometer based on the surface plasmon effect was developed. The adequacy of the obtained conclusions was confirmed by means of computer modeling and experimental research. The design of a means of measuring small concentrations of dissolved substances, built on the basis of the described sensor, has been developed. It is shown that such a measuring tool will be characterized by relative simplicity of construction while preserving all the advantages of the refractometric measurement method. [ABSTRACT FROM AUTHOR]