Apparently it isn't all that straightforward in this case. It appears to be right not to use "the". Some good explanations here https://www.quora.co m/Which-is-correct-“at-the-university”-or-“at-university”
It is correct both ways. In my (western USA) dialect of English, we'd say "I study English at the university." That's the only way I'd ever say it. But, in some other dialects of English, they do say "I study English at university."