A classic interplanetary romance, written as a serial for Astounding back in 1950 and showing it's age. Yes, the hero Dirk Barnevelt with trusty sword in hand is off to rescue and eventually marry a princess. The story does have an incredible amount of paternalism, intelligent woman described as bright, young girls, women soldiers worrying about not attracting husbands because they're too masculine and the topper, matriarchy is an unstable form of government. After all, men were meant to rule! Unlike Burroughs though, the issue of children is solved via a solution that reminds a me bit of the Pirates of Penzance, so Dirk's princess doesn't lay eggs
On a positive note, de Camp doesn't subscribe to the 40/50s SF trope that space travelers must be WASPs (White Anglo Saxon Protestant) and the tongue in cheek humor with which the story is told takes some of the sting out of the sexist bits. The author had writing career that lasted more than half a century, and in his later books he lampoons the classic formula, in at least one, the princess rescues the prince, along with other silliness.
The book is a well paced adventure novel and de Camps characters are a bit better fleshed out than his contemporaries, if you're looking for a 50s example of interplanetary romance, give it a try.