In 1868, the Moscow Crafts School was transformed into the Imperial Moscow Technical School, which became a higher specialized educational institution with a nine-year training program.

According to the first paragraph of the Charter, the school was intended for training mechanical builders, mechanical engineers, and engineering technologists. Among the first departments were those of higher mathematics, general and applied physics, mechanical engineering, construction art, technology of fibrous materials, general chemistry, and chemical technology.

By the end of the 19th and the beginning of the 20th century, the significance of IMTU in the technical and scientific life of the country had greatly increased. Fundamental scientific schools began to form at the school, driven by the rapid development of industry and the involvement of leading scientists, predominantly graduates of Moscow University.

By the beginning of the 1895/96 academic year, 656 students were enrolled at the school. From 1870 to January 1, 1895, 975 people completed the course. The school had a laboratory, physical and mechanical classrooms, a natural history room, a geodesy room, training workshops, and a library with 11,056 titles.

The Imperial Moscow Technical School had the right to confer the title of mechanical engineer from the engineering-mechanical department and engineering technologist from the engineering-technical department. This title was awarded to both the best students who successfully completed the course and to external individuals after passing exams with the appropriate educational certificate.

In 1930, the school was named after the revolutionary Bolshevik N. E. Bauman, who was killed on October 18, 1905, by a worker from the Shchapov factory, Nikolai Mikhailin. This occurred near the main building of the school, which was later named in his honor, at the corner of German Street (now Baumanskaya) and Denisovsky Lane.