This actually isn’t a library anymore. But it used to be one, and it still proclaims as such over the doorway!
Built in 1899 by a couple of Madison’s leading benefactors, the “Romanesque-Gothic” [ed: or Richardsonian Romanesque; see comment below] building was a library until 1969, when everything moved a few blocks to the library’s current home. Nowadays, the inside has been renovated (to its original glory, I’m sure), and it serves as the Museum of Early Trades and Crafts.
Reference:
Cunningham, John T. (1998). Images of America: Madison. Arcadia Publishing: Dover, NH.