Burn by Patrick Ness
In 1956 Sarah Dewhurst's father shocks her by hiring a dragon to work the farm. The dragon is a smaller blue rather than the traditional larger reds, though even the reds are now scarce. When the blue dragon, Kazimir, unexpectedly saves Sarah and her friend Jason Inagawa from the attentions of the racist police deputy, Kelby, everything changes. Sarah is part of a prophecy and she must escape the clutches of Malcolm, an assassin from a Believer Cell, the dragon-worshiping cult. When Sarah, Malcolm and Kazimir eventually converge, they are thrown into another universe, where dragons seem never to have existed. Can they save this world and the one they left?