This one's kind of an odd entry in the Heinlein catalogue, but it's less odd if we recall that he wrote some fantasy/horror stuff in the early 1940s.
Ostensibly it's a sword-and-sorcery adventure/fantasy. But since it was written by Heinlein, it overturns and undoes quite a few of the usual fairy-tale cliches. The ending, for example, exemplifies Heinlein's own non-fairy-tale take on what really constitutes living 'happily ever after'.
The Hero is one Evelyn Cyril 'E.C.' (and eventually 'Oscar') Gordon, a veteran of a long and unpopular war in Vietnam. (Major prognostication success here: remember, Heinlein published this in _1962_. And the Heinlein who had devoted _Starship Troopers_ to exploring 'why men fight' manages to deal pretty sympathetically here with the corollary question of why some don't.) Gordon hooks up with a Heroine -- Star, Empress of the Twenty Universes, who needs some help recovering the Egg of the Phoenix.
Heinlein gets to show off his swordsmanship a bit (like David Lamb, 'The Man Who Was Too Lazy to Fail', he was a champion swordsman at the naval academy). He also gets to have a little fun with a monster or two.
And -- it wouldn't be Heinlein without this part -- he takes the reader on a guided tour of some cultures whose mores differ from those of Middle America, by way of illustrating that (most) morals are _customs_ relative to time, place, and social milieu.
Well, it's a pretty enjoyable romp through a world of fantasy, and there's enough of Heinlein's signature on it to keep it interesting even for those of us who aren't into the dungeons-and-dragons stuff. But _Lord of the Rings_ it ain't, and this sort of thing is definitely not Heinlein's strength.
Readable, pleasant, diverting, and fun, and it's right on the money in its exploration of the _sense of adventure_. Nothing really groundbreaking, though, and it's interesting mainly because it's Heinlein.