From Wikipedia:
There is little information about his life. It is not known where he was born. Andrei Rublev probably lived in the Trinity-St. Sergius Lavra near Moscow under Nikon of Radonezh, who became hegumen after the death of Sergii Radonezhsky (1392).
The first mention of Rublev is in 1405 when he decorated icons and frescos for the Cathedral of the Annunciation of the Moscow Kremlin in company with Theophanes the Greek and Prokhor of Gorodets. His name was the last of the list of masters as the junior both by rank and by age. Theophanes was an important Byzantine master who moved to Russia, and is considered to have trained Rublev.
Chronicles tell us that in 1408 he painted (together with Daniil Cherni) the Assumption Cathedral in Vladimir and in 1425–1427 the Cathedral of St. Trinity in the Trinity-St. Sergius Lavra. After Daniil's death Andrei came to Moscow's Andronikov Monastery where he painted his last work, the frescoes of the Savior Cathedral.
He is also believed to have painted at least one of the miniatures in the Khitrovo Gospels.
The only work authenticated as entirely his is the icon of the Trinity, ca. 1410 (shown at right), currently in the Tretyakov Gallery, Moscow. It is based upon an earlier icon known as the "Hospitality of Abraham" (illustrating Genesis 18). Rublev removed the figures of Abraham and Sarah from the scene, and through a subtle use of composition and symbolism changed the subject to focus on the Mystery of the Trinity.
In Rublev's art two traditions are combined: the highest asceticism and the classic harmony of Byzantine mannerism. The characters of his paintings are always peaceful and calm. After some time his art came to be perceived as the ideal of Church painting and of Orthodox iconography.