Jasper, a five-year-old ginger cat who lost its left hind leg in a car accident and was abandoned by his owners, was adopted by deputy librarian Simon Frost from a rescue centre.
It became popular among students after Frost took it to work one day, and a recent "tea with Jasper" event attracted 140 cat-lovers.
Similar events are planned as Jasper is now the library's "official mascot".
"He is bouncy like Tigger, because he has three legs, and he is a bit unstable when he moves slowly - so he goes everywhere at speed," Frost told the BBC.
Jasper now has his own hashtag - #economicscat - and frequently makes announcements about the library on social media.
There is also a university "cat club" on Facebook, where students who are missing their pets can share photos of them with other cat lovers.
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