Say you get a call on your mobile asking 'Where are you?'
You'd say 'I'm studying in the university library'. (That's if you in there at the time, you see.)
Then say you met someone you'd not seen for a long time. He asks what you're doing at present.
You say 'I'm studying at the university'. (That presupposes he'll know which university you mean - otherwise, say 'I'm studying at university' or 'I'm at university' (he'll guess you're studying there), or 'I'm studying medicine at Manchester University'.)
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