Separately I've written a review of "Michael Kohlhaas", the principal work in this collection, so I'll pass it by now and comment on some of the other stories and Kleist himself.
Famous for his striking first paragraphs, Kleist begins "The Marquise of O" with the marquise placing an ad in the local paper asking that the man who fathered the child she is carrying to identify himself. The absurdity of this proposition might be something out of Kafka or Beckett or a contemporary writer, but of course Kleist wrote it in 1806. He then demonstrated his unusual talent for marching absurdity along the path of straight-faced realism while powdering it with sympathetic touches of romanticism. He was a tale-teller, a clue-dropper, and something of an antiquarian, meaning his work often indulged in the magic of times past, of legends, of miracles. In this sense, he was a very early bridge figure between the 19th and 20th centuries, at one and the same time ironic and tender.
In my edition, which I don't find listed in Goodreads, Thomas Mann's introduction suggests something special about Kleist's style, in German, that was essential to his trickery: he burnished his prose to the point that the reader would glide across it quickly while at the same time constantly being caught on its prickers. Emotion wells in all of these stories, likewise violence. In "The Earthquake in Chile", Kleist commences by noting that just as the earthquake struck, Jeronimo Rugera was standing next to a pillar in his prison cell, preparing to hang himself. In "St. Cecilia or the Power of Music," Kleist commences by placing four brothers in Aachen, determined to start a riot in protest against the Catholicism of the Convent of St. Cecilia. In "The Engagement in Santo Domingo," perhaps the scariest of Kleist's tales, he commences by introducing the fierce African Kongo Hoango mercilessly leading a revolt against the island's French whites.
All of these stories, as I commented in my review of "Michael Kohlhaas," achieve compression and excitement by being "told," not "shown," exactly what contemporary critics and creative writing teachers most abhor. But it is the "once upon a time in a strange place" quality of Kleist's fictions that making "telling" work--along with that steel smooth style of his. "The Duel" is dense with period-piece detail while hurtling improbably toward the enigmas of God on the one hand and lascivious chambermaids on the other. It relies on the power of honor and shame that even today does not need explaining even if duels are a thing of the past; that power can simply be assumed. Of course, men would fight over such slanders and insults. Of course, there'd be a naughty woman behind it all and a virtuous widow almost forced to pay the price for the wench's mischief.
There are writers like Pushkin and Kleist who are revered in their native tongues but not valued quite so highly in translation. Kleist's peculiar appeal to his German-speaking audiences (Kafka loved him) derives, I suspect, not only from his painstakingly revised prose but also from his intimate insights into the hypocrisies of pre-unification Germany and pre-dissolution Austro-Hungary. He stands nobility, justice, passion, loyalty, and pomposity on their heads and makes them look convincingly silly. He writes exactly what he knows people think but don't say, and that's what made Kafka laugh so hard. But at the same time, Kafka's protagonists suffer passively while Kleist's, venting his own anger, I suspect, fight hard...or, as often happens, they faint, a kind of trope in Kleist that mostly affects women overcome by the nauseating truth of things but occasionally affecting a man, even killing one...by fainting!
The key to Kleist, I think, is that you take him seriously by not taking him seriously. You laugh even if you aren't in on all the private German riffs. You know that because he is so strong, so headlong, so compelling, he is fully aware of what he is doing when he blows up conventions with nary a hint of puckishness.
Evidently he was miserable, shy, and unhappy most of his life. He had the wild notion that somehow he could supplant Goethe in the pantheon of German literature. But we should forgive him that. Kleist at his wildest is Kleist at his best. (Likewise Goethe, I might add.)