Asimov, Isaac. Foundation's Edge (Garden City, N.Y.: Doubleday, 1982) 366 p.
The Trantor University Library is mentioned, but now it is called the Galactic Library. First in the imagination of a historian who wants to study there.
The Library was outmoded and archaic—it had been so even in Ebling Mis's time—but that was all to the good. Pelorat always rubbed his hands with excitement when he thought of an old and outmoded Library. The older and the more outmoded, the more likely it was to have what he needed. In his dreams, he would enter the Library and ask in breathless alarm, “Has the Library been modernized? Have you thrown out the old tapes and computerizations?” And always he imagined the answer from dusty and ancient librarians, “As it has been, Professor, so is it still.” (p. 35).
Also, members of the Second Foundation discover that all references to Earth have been removed from the Library.