Listen: Kurt Vonnegut (1922-2007) was an American science fiction writer. His work is known for its satirical, anti-authoritarian, humanist, and often brutally depressingworldview. If this worldview can be pinned down to one event, it would be the bombing of Dresden.Vonnegut served in World War II. When in Germany he was captured by the enemy and brought to Dresden. Dresden was a large German town known for its doll-making that had little to no strategic military significance, yet was still fire bombed by the Allies into a smoldering charred pile. So it goes. This event would become a major theme in many of his books, especially the later ones.Vonnegut is also notable because he was one of the first modern science fiction authors to get serious attention in the literary world. Although your literature professors (and Vonnegut himself) may try to tell you he's not actually a science fiction writer, the aliens and time-travel seem to disagree.
The Verse: Vonnegut's stories and characters have a tendency to overlap with one another. If it's one of his fictional works, expect at least a cameo from Kilgore Trout and/or the Tralfamadorians.
Slaughterhouse-Five is a major offender of this, with Billy Pilgrim meeting several other protagonists: Eliot Rosewater (God Bless You, Mr. Rosewater) appears in the neighboring bed to Billy when he's institutionalized; Howard W. Campbell (Mother Night) is the Nazi American trying to convince the PO Ws to change sides; and both Kilgore Trout and the Tralfamadorians (pretty much every book) both meet Billy at some point.
White and Grey Morality: Despite his brutally cynical worldview, Vonnegut also wrote in the introduction to Welcome to the Monkey House that there were no villains in his stories, just people with conflicting interests.
Examples of tropes from his other stories
Brown Note: A radio telescope in "The Euphio Question" picks up "the music of the spheres", which gives such pleasure to listeners that they stop whatever they're doing, and only snap out of it when the playback is interrupted.
Death by Sex: Specifically cited in "Welcome To The Monkey House" (the short story itself, not the collection that borrowed the name).
Graceful Loser: In "EPICAC", the eponymous machine's response when it is told that it would never be able to be with the woman that it and its operator are competing for? Wish the operator well and commit suicide by overtaxing itself... writing thousands of love poems for him to give to her.
Gravity Is Only a Theory: In Slapstick, the protagonist and his sister theorize that gravity was once variable, which is how the Pyramids in Egypt were built. This turns out to be true when their theory is used by the Chinese to change gravity back to how it used to be. From that point on it varies daily.
Sadistic Choice: In "All The King's Horses," the captain at one point sees the one way he can save all but one of the remaining Americans... but he has to choose one of his twin sons to die. Due to intervention from one of his adversary's concubines, the child doesn't have to die.
...I am going to sue the Brown and Williamson Tobacco Company, manufacturers of Pall Mall cigarettes, for a billion bucks! Starting when I was only twelve years old, I have never chain-smoked anything but unfiltered Pall Malls. And for many years now, right on the package, Brown and Williamson have promised to kill me. But I am now eighty-two. Thanks a lot, you dirty rats. The last thing I ever wanted was to be alive when the three most powerful people on the planet were named Bush, Dick and Colon.
Strange Syntax Speaker: Haitian Creole is said to only have a present tense, leading to some very odd grammar. Of course, it's implied that the Haitians simply don't bother trying to teach the American proper grammar.
"He is dead?" he said in Creole. "He is dead," I agreed. "What does he do?" he said. "He paints," I said. "I like him," he said.
Interrupted Suicide: Fred Rosewater is about to hang himself, but he's stopped by a visit from Mushari.
It's Not Porn, It's Art: To settle once and for all the question of which is which, Senator Rosewater has created a law of which he is quite proud. The law says that if it has pubic hair, it's pornography. (Note that this was before the modern custom of porn stars shaving off their pubic hair).
Anachronic Order: In this case, due to the scraps of paper from the "original artist" getting a bit mixed up.
Gosh Dang It to Heck!: The narrator never swears, because his grandfather told him that if he uses profanity, it's easy to dismiss what he's saying.
Take That: At one point the narrator receives a pamphlet titled The Protocols of the Elders of Tralfamador (with Tralfamador being an alien planet), obviously a mockery of the anti-Semitic tract The Protocols of the Elders of Zion.
A Real Man Is a Killer: Vonnegut told this story many times, both in speeches and in at least one book other than Timequake. After he returned from World War II, his Uncle Dan came up to him and clapped him on the back, proclaiming "You're a man now!" The implication being that the only way for a boy to become a man was to kill people. Although Vonnegut had never had occasion to kill anybody during his military service, he had seen a lot of death and lived through the firebombing of Dresden, which wasn't a lot of fun. Imagine that you've just gone through the worst, most traumatic experience of your life, and before you've finished dealing with that trauma somebody comes up to you and congratulates you on it. Yeah, Kurt wanted to kill the guy.
Armageddon In Retrospect
Hypocritical Humor: His son, Mark Vonnegut, wrote the foreward for this book and recounts this exchange from one of his last conversations with his father:
Kurt: How old are you, Mark? Mark: I'm fifty-nine, Dad. Kurt: That's old. Mark: Yes it is, Dad.