Another book down on the "Great Heinlein Rereading" project. Specifically, rereading my first edition, purchased back in 1984. It is one of the "Late Heinlein novels", but (for me) it stands head and shoulders above his other books in that phase.
Back in 2010, I listed it as one of my "Ten Influential Books". And I'll just quote my plot summary from there:
It tells the story of Alexander Hergensheimer, who's far from the typical Heinlein hero. In fact, he's kind of a jerk. But he's roped into walking on fire in Polynesia, and (somehow) this starts bouncing him back and forth to multiple universes, where he meets Margrethe, the love of his life; it makes Lost look like a missed turn on the way to the supermarket.
(Kids, Lost was a TV series that ran from 2004 until 2010.)
Expanding some on that "multiple universes" bit: it becomes evident (page 2 spoiler) that Hergensheimer's "home" universe isn't ours. And neither is the one he gets initially bounced to. But (to his great fortune) he gets involved with the lovely Margrethe, a hostess on the cruise ship on which he tries to get back to (his) America. She (somehow) gets caught in his odyssey, travelling with him to each successive universe. And they fall in love.
What's going on? I won't even hint at it. But there's a big clue right on … nope, I won't even do that.
Influential? To me, yes. I got married not long after reading it the first time. I'm pretty sure this book cured me of my gamophobia.