I can't recall having read more absorbing stories, being so completely immersed, time and again, in different characters' worlds. As others have mentioned, each story is like a mini-novel, vivid, rounded, and fully dimensional. And even for someone who doesn't use the word "masterpiece" lightly, I believe it's entirely appropriate for this volume and its individual contents. One story, "Bad Neighbors," has a character named Derek as vivid as any in Shakespeare, as palpably real as someone you met this morning. "Common Law" views a brawling couple from the eyes of neighborhood children; "Tapestry," set within the depths of rural Southern poverty in the 30s (with magazine covers used as wallpaper), manages to be elegaic, with an elegance of style befitting its characters' essential dignity.
The best short story collections I can remember offhand are Hemingway's, Maupassant's, Chekhov's, Tillie Olsen's, and Joyce's. These are their equal, if not superior. Jones's work in "All Aunt Hagar's Children" truly stands out and demands to be read and appreciated for its depth, humanity, and literary excellence. It's a collection that will stay with you long after you've turned the last page.