An analysis of the well-known distance education systems was made, which allowed us to highlight their advantages and disadvantages and identify some ways to improve the program by adding adaptive functionality and interactivity, aimed at improving the educational process quality. An interface for working with the system for different groups of users (students, teachers, developers) has been developed whose use allows you to download study materials and test tasks conveniently, to edit and adapt some meaningful links between information sections (Units), to pass training and test control, to form final reports of success and recommendations for further learning steps. The multi-set method of assessing the level of study of content units was described and the adaptive functionality of forming the content of educational lectures for review or in-depth mastering of the theoretical content was presented, which allows taking into account the initial level of student knowledge and his/her abilities to acquire new skills. The software has been improved with a system based on PWA (Progressive web app) technology, which has allowed us to realize such advantages of web applications as speed, convenience, and attractiveness. A technology of text questions and correspondent information units connection was proposed which was based on the theory of multiple approach use which has provided us with the mathematical determination of the indices of the unmastered pieces of knowledge which generate the text part of the adaptive training step. Implementation of PWA technology was performed using the following software tools Service Worker, Web App Manifest, HTTPS, and Application Shell, which allowed to perform client caching offline, speeded up the process of downloading and displaying graphic elements of the web page, provided the use of the proposed resource as a regular mobile application. It has made it possible for easy access to the system to be obtained as well as the system resource use to be reduced.