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Racially and culturally, the forerunner of Russia was the Grand Duchy of Moscow (1263–1547) which later became the Tsardom of Russia under Ivan IV (The Terrible), and not Kievan Rus as has been claimed by Russian historians since the time of Catherine the Great (who, by the way, was not Russian).
Already by the end of the 15th century, the Grand Duchy of Moscow was populated mostly by Christianized Tatar-Mongols who in the course of the previous two centuries had gradually adopted Orthodox Christianity and taken Slavic names. The indigenous Slavic population had become a minority in a relatively short period of time due to the large influx of these Christianized Asiatic nomads, and due to mixed marriages between Christianized Mongols and indigenous Slavs.
The expansion of the Grand Duchy of Moscow further to the east, into the lands of Ugric peoples (e.g., Mordvins, Udmurts), increased the Asiatic component of the population even further. Later, under Ivan the Terrible, the Kazan and Astrakhan Khanates were conquered and incorporated into the Tsardom of Russia. The vast majority of the Volga Bulgars populating those states (whose descendants from the 19th century on were falsely called “Tatars,” not to be confused with the nomadic Tatars mentioned above), was forced to adopt Christianity and Slavic names. And finally, beginning with the conquest of Siberia in the 17th century, there was a gradual Christianization and Russification of the mostly Turkic peoples populating those lands.