When I first began learning Ukrainian, I assumed that it was essentially a dialect of Russian. After all, Russia and Ukraine have a long history together, and the question of dialect versus language is a tricky one. Generally, it is agreed upon that if you understand perfectly, you speak the same language. If it takes some effort to understand, then you speak different dialects of the same language. If you cannot understand at all, you speak a different language. It's as simple as that.
Unfortunately, Ukrainian doesn't fit neatly into one of these three molds vis-à-vis Russian. The languages are certainly related; according to my professor, a Russian who has been exposed to Ukrainian can usually figure it out. However, the languages are sufficiently different that a Russian from, say, Siberia, who has never met a Ukrainian person before, will probably not be able to understand.
I have proof of this notion. A friend of mine at Pitt grew up speaking Russian with her parents in Brooklyn, but was never exposed to Ukrainian. When I asked her if she could understand Ukrainian, she said she could to a certain point, after which it becomes too garbled. According to her, a Ukrainian speaker sounds "like a Russian who has been punched in the mouth." On the other hand, her father, who grew up in Belarus, can understand Ukrainian perfectly.
The reverse is also true in theory - Ukrainians who have heard Russian before should be able to understand it, while those who have not, should not. But in reality, nearly every Ukrainian can speak Russian fluently, so it's not a very relevant point to make. Indeed, some of the only people in the world who know just Ukrainian are students like me, who have taken or are taking the language outside eastern Europe. My professor even warned us that our knowledge of Ukrainian may be more "correct" than many native speakers', simply because our ears haven't been tainted by Russian.
Another interesting point: because Russian is so pervasive in Ukraine, a sort of creole language has become popular in many parts of the country. My professor, who is from Kharkiv, says that this mixed language is mostly found in the east. In the west, there are more people who speak Ukrainian at home (as opposed to Russian, or the mixed language), so there are many more "pure" speakers.
Someone once told me that a language is simply a dialect, plus an army. In the case of Ukrainian's relationship to Russian, this probably isn't true. All modern linguists agree that Ukrainian and Russian are separate languages that diverged from a common source many centuries ago. (To be specific, during the 13th century, two major dialects of Rus began to arise. The northeast dialect was the basis for the future Russian language, while the southwest dialect was the basis for the future Ruthenian language, which in turn developed into Ukrainian.) Nevertheless, from a historical perspective, the Ukrainian language has served both as a galvanizing factor motivating people who believed in the need for an independent Ukraine, and as a source of contention for those seeking to diminish the prospects for Ukrainian statehood. What a unique, complicated situation.
Was it prudent for me to take Ukrainian this summer, given that Russian is often the more popular spoken language in Ukraine? If my goal had been simply to speak to people in Kyiv and Chernobyl, then probably no, it would have been wiser to take Russian. But I also took this class to get a feel for Ukrainian culture - how Ukrainians think, what to expect from the nation and its people. I am learning that, so I do not regret my decision.
Plus, as Ukraine becomes a more powerful nation, and more and more schools start to offer the language, and more and more students decide to learn it, then my Ukrainian skills should prove very useful - maybe even invaluable - in the future!