illy Pilgrim first became unstuck in time when he was caught behind German lines during World War II. He was leaning against a tree when suddenly he found himself traversing his entire life, from his bubbly beginnings in the womb to the final end, which was simply a violet light and a hum. During that first unsticking he experienced quite a few things, including the time he was a little boy and his father tried to teach him how to swim by tossing him into the deep end of the Y.M.C.A. pool.
This kind of thing went on a lot throughout the war as well afterwards, with Billy going forward and back along his life, a process he had no control over. It even continued after he was kidnapped by a flying saucer the night of his daughter's wedding, which of course he knew would happen thanks to the unsticking thing. The Tralfamadorians, as the aliens called themselves, took Billy back to their planet where they kept him on display in a zoo. Eventually they added Montana Wildhack, a former porn star, to his simulated Earthling habitat, which was furnished with items stolen from the Sears Roebuck warehouse in Iowa City, Iowa. Montana was a pretty good person to make babies with, which is just what she and Billy did after she settled in.
Although the Tralfamadorians returned Billy to Earth and explained to him how they experienced time--"seeing all time as you might a stretch of the Rocky Mountains"--he never mentioned the aliens to anybody until after the plane crash that caused his head injury. Needless to say, no one really believed him.
It's great, but is it SF?
At its heart this is a book about the bombing of Dresden, Germany, during WWII, an attack that killed more people than the dropping of the atomic bomb on Hiroshima. Like Billy, Vonnegut himself was a prisoner of war in Dresden during the attack, and he was one of the few people to make it out of the city alive. As the first sentence of the book says, "All this happened, more or less."
So the story of Billy is not about time travel and aliens per se but about his attempts to cope with the horrors he witnessed in Dresden. Those attempts, of course, involve retreating from the world by becoming unstuck in time and by being safely ensconced on Tralfamador. Because all of this takes place in Billy's head, Slaughterhouse-Five is not overtly an SF book, but rather a book about a fellow with delusions of flying saucers and aliens.
But even if Slaughterhouse-Five is shelved in the literature section--and even if Vonnegut himself shies away from the label "SF writer"--this is an important work of science fiction. Like many of Vonnegut's novels, it reveals insights into human nature through a speculative journey in time and space, and whether the Tralfamadorians exist only in Billy's head or not is entirely irrelevant to the story. The journey and what it teaches readers is the key element of Slaughterhouse-Five.
In the end this must be considered one of the enduring works of any genre, and it is a book no reader should miss.