Wooohoo, thanks a lot for the great explanation, TATY!
You got me to start understanding a point that has always been really confusing to me: The dative being used after reflexive verbs. I was always like when I saw sentences like Я учу Джона русскому языку - I am teaching John Russian or Я учусь русскому языку - I learn Russian. It always looked so strange to me, now I think I get it.
Can I say something like "Я учусь русскому языку на филологическом факултете"?

Eeh, that dative construction gets confusing to me when I think about, for example, how would someone say "I study for the Russian test"?