In one of the intensely imaginative stories in Rivka’s Galchen’s American Innovations, a young woman’s furniture walks out on her. In another, the narrator feels compelled to promise to deliver a takeout order that has incorrectly been phoned in to her. In a third, the petty details of a property transaction illuminate the complicated pains and loves of a family.The tales in this groundbreaking collection are secretly in conversation with canonical stories, reimagined from the perspective of female characters. Just as Wallace Stevens’s “Anecdote of the Jar” responds to John Keats’s “Ode on a Grecian Urn,” Galchen’s “The Lost Order” covertly recapitulates James Thurber’s “The Secret Life of Walter Mitty,” while “The Region of Unlikeness” is a smoky and playful mirror to Jorge Luis Borges’s “The Aleph.” The title story, “American Innovations,” revisits Nikolai Gogol’s “The Nose.”By turns realistic, fantastical, witty, and lyrical, these marvelously uneasy stories are deeply emotional and written in exuberant, pitch-perfect prose. Whether exploring the tensions in a mother-daughter relationship or the finer points of time travel, Galchen is a writer like none other today.