It adopted a resolution in 1795 "that the object of this Society is the collection of an extensive Library, philosophical apparatus and such products of nature and art as tend to improve the mind and excite a spirit of general enquiry".
The society declined in the later 1790s however, as it owned no permanent premises and struggled with official attempts to control radical thought, though it survived a crackdown after the 1798 rebellion thanks to the efforts of Rev.
Investment in public libraries combined with extensive IRA bombing in the city centre led to membership levels falling.
By the end of the 1970s the Library was on the brink of closure, with large amounts of material (including an extensive collection relating to The Troubles) but a poor building, few users and serious money problems.
It was decided that it should begin to allow and encourage free public reference access and to concentrate particularly on Irish studies, politics and culture, both because it was already strong in these areas and so as not to compete with Belfast Central Library.
After spending ten years exploring various options, a decision was made to purchase a 999-year lease on the upper floors of some neighbouring property in 1996.
A choir consisting of students from Holy Cross Boys' Primary School and Campbell College performed for the guests of the notable event.
It is the leading centre for "Irish and Local Studies" in Northern Ireland which includes its comprehensive stock of "Early Belfast and Ulster printed books", periodicals and newspapers dating back as far as 1738 and a wide variety of archive and manuscript material.