Mishnah Bava Metzia 2:8 (this is in the chapter discussing the laws of returning lost objects to their rightful owner; cf. Deuteronomy 22:1–3):
Someone who finds [lost] scrolls should read from them once every thirty days. And if he does not know how to read, he should roll them. But he should not learn from them at first, and another person should not read with him….
Once every thirty days, because they will grow moldy if left unopened, and all their scrolls were made like one sheet. Roll them, from beginning to end, to let the air in. At first, something that he never learned before, because he will have to leave them before him….
Ikkar Tosefot Yom Tov:
These words apply to books of Scripture, because for someone who has already learned them, it is enough to just read them, but someone who is learning them for the first time needs to make a great effort, and this effort damages the scrolls. But now that we write the Oral Law, and someone who learns a chapter of it a hundred times needs to study it in great depth like in the beginning. On the contrary, anyone who is a great expert needs to study in great depth the laws he needs to learn, and he is like one who is learning for the first time. [Thus says] Netzach Yisrael in the name of Nachmanides.
tl;dr The proper way to care for a book, even a book that belongs to someone else, is to read it. How very Jewish.