Looks goo! Just some bad grammar: UniversitIES exist or University existS

Universities exist... or University exists... "Advance knowledge" is a bit vague - it bakes the question of "whose knowledge is being advanced". So a well-educated mature scholar would usually avoid speaking like that. To be a bit more clear, you could say "advance our knowledge and educate us" or "advance people's knowledge and educate them". But advancing our knowledge is pretty much the same thing as educating us, so why say it twice? So you could simplify like "Universities exist to educate people" or you could expand to something like: "Universities exist to educate us. Advancing our knowledge, and improving our lives."