Final answer:
"The Murders in the Rue Morgue" was Poe's first detective short story, published in 1841.
Step-by-step explanation:
The name of Poe's first detective short story is "The Murders in the Rue Morgue" and it was published in 1841.
Poe is considered the father of detective fiction and this story introduced the character of C. Auguste Dupin, who is often credited as the prototype for the modern detective. "The Murders in the Rue Morgue" follows Dupin as he solves a baffling mystery involving a brutal murder.
This story is significant because it established many of the conventions and tropes of detective fiction that are still used today.