The Cat Who Walks Through Walls

The Cat Who Walks Through Walls is subtitled "A comedy of manners." A lot of really bizarre things happen to the main characters. They react to them in a matter-of-fact way. (The opening starts with a guy sitting down next to the main character and asking him to kill a guy. Then the guy is suddenly killed himself. The restaurant staff quickly cleans things up, and nobody in the restaurant even seems to notice.) Later the guy and his soon-to-be-wife find themselves locked out of their apartments and just go with the flow as they have to move.

Things gradually get weirder and weirder. There is some time travel group that goes on alternate histories. They save people from all sorts of bizarre things so that they can influence future events. Some alternate paths turn out worse than the one they were trying to avoid. (For example, preventing a tyrant may actually lead to global destruction in a nuclear war.) Different key events may happen in different ways in different alternate histories. We also get computers that become self-aware and a number of Heinlein's political beliefs (free-love military conservatism.)

This contains a number of similar characters of other books such as Moon is a Harsh Mistress. While it starts out with some interesting story, that gets lost in the final 3/4s of the book as more space gets spent on the random beliefs and just plain randomness.