Explanation:

- A Restaurant offers food based on a Menu. The menu lists all the food options available in the restaurant.

- Similarly, a Library offers books and other materials to read.

Let's evaluate the options:

- Register: A register could be used for logs but is not directly related to library offerings.

- Rack: A rack is a physical structure for storing items but is not directly related to listing available items in a library.

- Book: While books are found in libraries, they are not a list or display of available options.

- Catalogue: A catalogue is a compilation that lists all the books or resources available in a library.

Catalogue is to library what menu is to restaurant.