"The book was sad."

Translation: Boken var sorglig.

[takver]

So 'ledsam' is like causing sadness, whereas 'ledsen' is feeling sadness?

[Zmrzlina]

Yep. It would sound weird to have ledsen describe an inanimate object.

[sustained]

I was under the impression that "sorglig" was more along the lines of "tragic" or "sorrowful" and that "olycklig" was more "sad"?

[Arnauti]

Like ledsen, olycklig is not used for inanimate objects in this context.
There is another context where it's used with inanimate objects, but then it gets the meaning 'unfortunate': Det var ett olyckligt beslut/en olycklig händelse 'That was an unfortunate decision/event'