Russian Music before Peter the Great

In the way of secular music, there were minstrils, or skomorokhi, who probably traveled and sang songs like minstrels in other countries. There isn't much (if any) in the way of musical sources surviving, because their craft was an oral tradition. So all we can do is conjecture based on iconography and knowledge from similar people in other countries (like the troubadours of France). Once the Orthodox church took over the dominant position in Russian music, the skomorokhi were persecuted and kept from having any major influence.
In the church, beginning with Vladimir of Kiev's 988 A.D. conversion to Christianity we expect to find chant, as that's what was going on most places at that point. We don't know much about this early Russian chant because the notation used in the surviving sources is (so far) undecipherable. Decipherable chant sources have been found dating back to the mid 1500s. Solely momophonic (znamenyi) chant existed through the 16th century. In the 17th century, a more florid chant called demestvennyi chant appeared. Due to its complexity it may have been intended for trained singers. Also in the 17th century polyphonic motets appeared. This represents the most significant penetration of Western Culture to this point, at least in music. These polyphonic pieces are based on the Venetian tradition and the style was transmitted by Polish composers who had been in Venice and returned to Poland. From there the tradition gradually spread through the Ukraine and into Russia. Who were these Polish composers? I don't know. Maybe I'll try and look them up.
So, the simple znamenyi chant, the more advanced demestvennyi chant, and the quasi-venetian polychoral motets constituted the extent of progress in Russian music through the time of Monteverdi, Gabrieli, Purcell and many other sophisticated European composers.
One other body of music exists also: rather dissonant polyphonic motets that seem to be based on folk music. The dissonance is such that it either represents a strange and astounding pocket of harmonic exploration somewhere in the 17th and 18th centuries, or today's scholars have not figured out how to transcribe the sources correctly.