The article presents a three-stage system of training the Russian language to foreign students in one of the renowned technical universities of the Russian Federation. The authors describe in detail the structure and content of the ten tasks for the admissions test in the Russian language, which constitute the materials for specific linguistic topics, the content of each module of the training program: grammar, conversation topics, number of hours allocated for the study of the material and midterm control, forms of classes, types of work of undergraduates. The authors note that from 2017 there has been conducted an experiment on the teaching of foreign graduate students in the new program. The article also describes its content and provides an example of assignments of the final exam in the Russian language. In addition, the paper presents the basic material used in the classroom – books on learning the Russian language: grammar, vocabulary, textual content, annotation, abstracting and modelling of texts of different types.