I really enjoyed this book from beginning to [almost] end. The reason for the "almost" will become apparent.
The story of time travel by various means was excellent. When reading this story, you should remember that it was written in the 1950s. Some of Heinlein's predictions are amazing, and some are way off the mark. It's amazing to follow his line of thinking though.
You can see an outline of the plot in the description. It is fairly predictable, but that didn't detract from my enjoyment of the story at all. It was fun, and it was refreshing to read such innocent prose.
Although some people might be offended, there was some narrative that would be considered non-PC these days, but was just part of life in the 'fifties. I actually found that quite refreshing too. I get so irritated by the over-sensitivity to political correctness these days. You can't even tell a good Irish joke, or drop your pants in a US bar to proudly show off your British tattoo, these days, without drawing comments from the puritans.
The story was great right up until the final chapter. This was a bit of a damp squib, Heinlein felt that his hero had to justify and explain his actions and how several instances of himself could coexist. I would have been far more satisfied with the explosive ending which could so easily have been there.
Having said that, I would strongly recommend this book to all lovers of time travel and sci-fi books.