Is the word 'library' a common noun or a collective noun?

The noun library is a common noun and a collective noun.

The collective noun library is used for a library of books, a library of records, and any extensive collection of other things collected by people.

The the noun library is a common noun, a word for any library.

A proper noun is the name of a person, place, thing, or a title; for example:
  • The New York Public Library
  • The Library of Congress
  • The Library Cafe, Farmingdale, NY
  • Library Street, Wigan, UK