Vasily I was the son of Grand Prince
Dmitry III of
Russia and came to the
throne on his father's death in
1389. He was a rather
cautious ruler who tried his best to balance the pressure from the
Lithuanians to the west and the
Mongols to the southeast. Vasily did visit the Mongols who were still the titular overlords of Russia for them to approve him as Grand Prince, but other than that he paid them little attention and did not collect
tributes to be paid to the Mongols for most of his reign.
Vasily continued his family's policy of increasing the amount of land controlled directly by Moscow instead indirectly through other Russian princes. The cities of Riazan and Tver were opposed to control from Moscow and their rulers tended to rebel, but Vasily generally managed to come out on top. Grand Prince Vitovt of Lithuania invaded western Russia several times, but Vasily managed to hold him off (sometimes with Mongol support) and in 1408 a treaty was made between the two governments. (After the treaty was signed, several princes along the border switched their allegiance back to Russia from Lithuania.) Nonetheless, a lot of territory then inhabited by Russian-speaking peoples was governed by Lithuania -- much of what is now Belarus and Ukraine.
Southern Russia was invaded in 1395 by Tamerlane, but those forces decided not to go as far as Moscow, so the country was spared another conquest. About 1400 the Russians attacked the Bulgars along the Volga River to try and rid themselves of another source of raids. Any in 1408 the Mongols sent a large number of troops, supposedly to Lithuania but in fact they mounted an attack on Moscow to extort the tribute they hadn't been getting. They didn't capture the city, but they devastated the surrounding area. At this point Vasily (who had fled the city at the actual time of attack) did start giving the Khan "gifts."
Vasily died in 1425 and left the throne to his only still-living son Vasily II, who was only ten at the time. (This appeared to be in contradiction to the will of Dmitry III which stated that Vasily's brother should succeed him, and started a civil war.)