Can I upload a Book to Arxiv which I have already Published?
It's very dangerous to say "I suppose I have already signed a contract". This is legal stuff. The exact wording is important! If you have signed a contract, take it out and read it. What exactly did you agree to?

The odds are good you'll have to ask the publisher about whether you can do this. Even if the contract said you can't do this, it's possible they'll still say yes, especially if they've stopped actively trying to sell the book. Nonetheless, they might impose other restrictions - for example they might say you can only post the raw manuscript (i.e. no redrawn figures, no title &amp; half-title pages if they were prepared by the publisher, no book cover [again if it was prepared by the publisher], no special fonts ...).

In any case asking the publisher is never going to be wrong, so I recommend doing that.