For the first one, usually you would use the here - you are thinking of a specific one, and you either expect the reader to know which one you mean, or intend by using the to convey to them that there is a specific one.
It is possible to use a, but it is unusual, and suggests something like "I didn't know this thing existed until that moment", with perhaps a bit of surprise that such a thing should exist at all.
For the book, both are possible. Using the suggests that you have some familiarity with it, whether or not your readers do; a suggests that you don't know it, or that you expect your readers not to have heard of it. There is not a clear separation between the two cases, though.