Chip Delany's 2nd novel -- the first is The Jewels of Aptor -- published by Ace Books in 1963. Set in the 35th Century, the survivors of a nuclear war live on the coastline and an island in a kingdom ruled by a royal family in disrepair. A young victim -- the son of a wealthy merchant -- of their wrath becomes a working-class hero as he fights to get back his good name, aided by a disaffected member of the royal family. This was later rewritten as Out of The Dead City by Delany as part of the Towers Trilogy, an early masterpiece, IMO.
