Why is it significant that the books in the library are real?
Gatsby has spent a fortune on his mansion in order to impress people and especially to make an impression on Daisy. Even though he is not well-educated, he has an impressive-looking private library in his home. It appears that he does not read the books but nevertheless has furnished his library with real books instead of economizing by filling up shelves with mostly cheap fake books that are nothing but dummies with gaudy gilt bindings. What this shows about Gatsby is that he wants very much to be genuine, the real thing, and not an imposter. He wants the books to be real even though he probably couldn't understand many of them and wouldn't enjoy many of the others. Nick is relieved and gratified to learn that the books are real because he has a good education himself and would feel somewhat tainted by associating with a real imposter who also has a shady reputation. Perhaps Gatsby really intends to read these books someday. He has always had aspirations to improve himself, not only socially and financially, but in every possible way. He is not only concerned about other people's opinion of him, but he is concerned about his own opinion of himself.