To study in Russia you need to get a student visa.
Applicants form the countries listed below don't need visa to study in Russia:
Applicants from the countries listed below can enter Russia using their national passport:
Applicants from other countries, including the CIS countries not mentioned above, need an international passport to come to Russia.
Even though Russia has visa-free arrangements with many countries, the duration of a visa-free stay is limited to 1 or 3 months, as such arrangements are designed for tourists, not long-term visitors. In theory, a student from a country which has visa-free arrangements with Russia can enter using only their passport, but after the permitted stay is over they will have to leave the country and re-enter it with a valid student visa. Therefore, it is simply better to get a student visa in the first place.