The sustainable development agenda is currently of great importance in all countries. One of the Sustainable Development Goals is to provide quality education (Goal № 4). The relevance of the topic is also explained by the implementation of the national project “Education” in the country. The article describes the current state of the educational system in Russia, paying special attention to school education, as well as the “bottlenecks” of higher education and shows the relationships between them. Finally, possible solutions to the problems described are presented, which would improve the quality of education in the country and thus enable significant progress in the implementation of the corresponding sustainable development goal. They essentially amount to adjusting the tasks of school education and changing the approaches to their implementation in universities.