A question of time travel and paradox.?

If your dog dies and in the future you make a time machine to go back in time to save him, will it work? Of course not, if you in fact made a time machine to save your dog, and were successfull in your attempt then why would your past self need to make a time machine to go back in the first place? Does anyone know of any good books that talk about the theories of paradox? I love the concepts of time travel and paradox together and am looking for a good read.