I read this back in the 1960s, on my initial round of Heinlein-devouring. That was a school library book, and I remember being kind of shocked that the Omaha Public Schools would think this sort of filth was suitable for young eyes. (Didn't stop me from reading it though.)
The pic/Amazon product link over there on the right is the same edition I now own. Apparently set me back a cool $2.50 back in 1984 or so; it has languished unread on my paperback shelves until now. One of the reasons for my Heinlein-rereading project, now with a mere 31 books remaining.
The narrator is Evelyn Cyril "Oscar" Gordon; as the book opens, he is rattling around Europe after an unpleasant hitch fighting an unnamed war for the US Army. While on a clothing-very-optional island off the French Riviera, he gapes at a stunning unclothed woman, who tells him he's beautiful.
Intrigued by a classified ad that promises adventure, he's surprised that the offer is made by the very same woman! He signs up for a perilous, complicated quest for the "Egg of the Phoenix". They, with her grumpy assistant Rufo, set out on their universe-hopping exploits.
What follows: magic, swordplay, fisticuffs, culture clashes, all incredibly dangerous. Plenty of PG-13 talk about sex, where 20th Century American mores are derided as hopelessly out of step with the rest of the universe. There are a lot of winking references to other fantasies: Tolkien, Carroll, Baum, and probably many others I didn't pick up.
This is literally fantasy, both in the usual sense, and also in the adolescent wish-fulfillment sense. What male American teenager doesn't want to take off on a wacky adventure with a gorgeous babe who routinely sheds her clothes?
That said, there are a few pages here, where Oscar is in battle with the guardian of the Egg of the Phoenix, I think are among the best passages of Heinlein I've read.
Here's an odd thing: once the Egg is retrieved, you've still got about 30% of the book left to go. This is filled with… not a lot of things actually happening. A lot of dialogue, a lot of monologue. It's not awful—it's Heinlein, after all—but I'm not sure that was a good call. Nobody asked me.