I'm still trying to figure out how this novel won a Hugo. The best I can come up with was that it was a VERY weak year.
Basically, Fritz Leiber's novel is a locked-room mystery rooted in a great premise. The idea of the Change War holds enormous promise, but here it's little more than the context for a much smaller story. This doesn't necessarily ruin the novel, but Leiber's slang-addled first-person narrative can make events a little difficult to follow. My advice is to stick with his far superior short story sequel, "Try and Change the Past," which does far more with the basic premise (and uses less to do so) than Leiber does in this disappointing effort.