1. He is reading a book at the library.

Question

2. He is reading a book next to the library.
3. He is reading a book in the library.
[What does #1 mean? Does #1 mean #2 or #3? Or does #1 mean both?]

Answer 1

For some reason I can't explain, 1 and 3 mean the same thing.

2 means that he is reading outside the library, maybe sitting or standing next to the wall of the building.