The permanent building, at the junction of Clarence Street and St Georges Place, replaced the temporary Free Library on the High Street. The Free Library opened in October 1884 and three years later the foundation stone of the current library was being laid. The new Library was designed by William Henry Knight and was opened on 24th April 1889. It boasts columns, balustrades, carvings, statues and a tower. The Library is attached to the Art Gallery and Museum, part of which is in the Library building.
Below is a photograph from the opening of the Library in 1889.
The other photos I've taken show more of the buildings detail. I'll post these when I find out more of the Library's history!