Was it like a modern university, where you need to have library privileges as an alumnus or a student to get access to the library? How did one gain access? Did you need a letter of introduction as one needed in the 18th and 19th Centuries?
More can always be said if anyone would like to address the internal processes of the Alexandrine Bookshop, so further posts from anyone who can contribute are welcome! For the meantime, OP, here are some previous posts that go some way to showing what the libraries were like back in that period: