This is book 3 of the "Barsoom" series.

This note contains spoilers for the book.

Messing around in the polar regions, finding the remaining "yellow men" of mars, rescuing Dejah Thoris and losing her before the battle to rescue her is even complete, running into old friends and the parents of old lovers right and left at key moments.

There are ups and downs, but in the end he and Dejah Thoris, together, actually get back to Helium. Then he's called to trial (he was released for a year by some rule or other), which turns out to be a ruse to surprise him in being appointed Emperor, or Jedak of Jedakks, or Warlord, or whatever it's called; the big boss.

So it actually manages to end with everything fine and rosy and everybody together and happy. I think I'll stop here.

A lot of what's said about Martian society in the first book doesn't pan out. Women being good fighters, but not fighting men anyway, for example (and training the men). Men not being sexually predatory. Lots of socially progressive ideas put forward, and then ignored.