This is actually the third of Poe's stories about Auguste Dupin, the first fictional detective, but it's the best one, and the most obviously gothic. The others are "Murders in the Rue Morgue" and "The Mystery of Marie Roget." Do not read the second, it's awful.
Here, Dupin must steal back a stolen letter that can be used to blackmail the queen, as she's carrying on an affair. The minister who steals it, only ever referred to as D--- (a method in 18th and 19th century writing of concealing a person's name), took it right before her eyes, as to protest the theft would be to reveal to her husband, standing nearby, that there's something worth stealing on her desk.
Now, you should read this story. It's extremely good. But if I tell you why it's a great gothic narrative I'll spoil the good bit, so here's the link, let's talk after:
OK, so here's the thing: the story very quietly leaves hints lying around and you can figure out, if you read very carefully, or, and I mean I did this, or if you read the essay in the back of the Norton Poe that argues this -- Dupin and the minister are brothers. "D---" is just "Dupin," the entire thing is a trick.
Dupin says the minister did him a bad turn once, in a tone that brooks no discussion; something bad happened. Dupin also says the minister will know his writing on sight, without needing a signature to figure out who wrote the note he leaves behind.
That means this is a doppelganger story, a common gothic trope since at least Hoffman's "The Sand-Man," though Poe is one of the most important vectors from which Anglophone gothic literature got the trope (apart from this story there's also "William Wilson").
Why it matters that this is a doppelganger story is that it's among the earliest detective fiction, which means that entire genre is about a person becoming a doppelganger of someone else, learning their habits and copying them in order to anticipate their movements and divine their secrets.
That's the good shit, my friends.