Ukrainian folk music has a very long history that dates back to Medieval times, before Russia as we know it even existed. We have numerous recordings of traditional Ukrainian folk music as it survives in our time, especially in the Alexander Street Press streaming audio database to which we subscribe. 
Alexander Street Press - Discover (unt.edu)

Spotify does not offer institutional subscriptions at present, but it is possible to listen to Spotify www.spotify.com whether or not you have a subscription. They currently offer a large number of recordings of Ukrainian music of various kinds, including folk music. Several playlists are available, which is helpful for listeners just beginning to get acquainted with Ukrainian music. 

YouTube has many examples of Ukrainian folk music as well. www.youtube.com

Major music reference sources such as Grove Music Online, available as part of Oxford Music Online Oxford music online - Discover (unt.edu), and MGG Online MGG online - Discover (unt.edu)--Die Musik in Geschichte und Gegenwart--have informative articles about Ukrainian folk music. Although MGG is a German encyclopedia, it now has Google translate imbedded, so you can read articles in English or many other languages.