If your boss won't return it your coworker is liable for getting you a new book as far as I'm concerned

Wow. Because when I see an expensive looking book on the table that I SHARE with another coworker I don't play it safe and assume it's theirs. Oh, oh, and it gets better, I give it to Boss because surely it's nobody else's. SURELY. Honestly, it sounds like they were trying to suck up to boss by giving an expensive gift without actually paying anything

I would make your coworker buy you another one. Why would he just assume it was his to give away when you share a desk. It's his fault more than anything. That sucks tho OP

Wow! People people stupid stupid

I saw this in random a few days ago???

Words fail me. The co-worker who gave your boss the book is not only a kiss ass and is also a jack ass for for just randomly picking up items and assuming they can be given away. Report to HR and threaten to get police involved as this is theft which ever way you look at it. OP please do a follow up

Get your coworker to vouch for you. If there is anyone above your boss in the company, go to them

So your coworker sees something sitting on a shared desk, has no idea who it belongs to or why it's there, and decides the most appropriate course of action is to give it away without asking? He sounds like a real peach.

isn't that theft?

The action of your coworker who gave the book to your boss is so obviously wrong I have to assume they knew exactly what they were doing and either out of spite or jealousy gave the book to your boss. That the boss wouldn't return it when it was explained to him implies that he is punishing you for some reason. You need a new job - You have a toxic coworker and a terrible boss. But let the book incident go at work until you find a new job because it's not worth getting fired or getting a bad recommendation over.