Before we launch into our plot analysis, we just want to say that the layout of "The Murders in the Rue Morgue" is unconventional. It's more like a mathematical proof than anything else. There's an equation to start out with, where analytical + imaginative mind is greater than analytical mind (A + I > A). And then there are two proofs. There is first a minor one, where Dupin guesses what the narrator is thinking after several minutes of silence. But then there is a major proof, where Dupin solves a horrible double murder that has baffled everybody else. Because "The Murders in the Rue Morgue" has those killings in the title, we've decided to focus on that plot line, but check out our "In a Nutshell" section and "Character Analysis" of Dupin for more on the story's long introduction.
The initial situation of the plot is the status quo, before we start getting into the mix of things. As the narrator and Dupin read about the deaths of Madame and Mademoiselle L'Espanaye, they collect a bunch of intriguing information (unusually brutal deaths, windows and doors locked from the inside, police baffled), but they don't start trying to put two and two together yet.
The guys were already interested in the Rue Morgue case, but it's not until the Le Bon arrest (based on the fact that he brought four thousand francs from Madame L'Espanaye's bank to her apartment three days before) that Dupin feels personally obliged to help solve it. He owes Le Bon some unspecified favor that tips his interest in the case, and the narrator comes along for the ride. Meanwhile, the narrator is baffled: he has no idea, based on what has been reported so far, how these two women could have been killed.
The complication stage is the part of the story where the conflict gets more intense. If the conflict in this story is that the narrator thinks the case is unsolvable and Dupin is trying anyway to solve it, then the complication must be the point when the narrator is at his most confused, and Dupin seems furthest from solving the case. This moment comes when the narrator and Dupin visit the death rooms, examining the corpses themselves, the rooms, the premises, and the neighborhood. The narrator expresses total confusion: he doesn't see anything that hasn't already been reported to the newspapers and logged by the police. And Dupin isn't talking at all. How is this all going to be resolved?
At noon the next day after visiting the scene of the crime, Dupin tells the narrator that a man is coming to the apartment who, while not actually the killer, has material evidence that will prove who the murderer is. Dupin has solved the case, and we're just waiting for the proof. The man is a French sailor from a Maltese ship, says Dupin. What's more, the murderer is an Ourang-Outang. The narrator is all astonishment.
Now that the climax has come and we know that Dupin has solved the case, we still have to wait on the edges of our seats for proof of how he has come to his conclusions. Dupin tells the story of what he saw at the scene of the crime, which led him to the conclusion that the killer is an Ourang-Outang. He's got proof of that bit through a comparison of the bruising on Mademoiselle L'Espanaye's neck to an account of the finger size of the Southeast Asian ape. What he's guessed about is that the Ourang-Outang's actions were observed by this famous sailor. So we have Dupin's solution (that's the climax) and the suspense is all in waiting for someone to support his claims.
The dénouement is the part of the plot where everything is resolved. It's here that we find out the proof of Dupin's final speculations. Yes, the Ourang-Outang belongs to a French sailor from a Maltese ship. The sailor explains that he brought the ape back to Paris to try to sell it, but that it escaped the night of the killings and, attracted by the light on in the open window of the L'Espanaye apartment, swung inside and killed both women. The sailor saw the murders, but has been reluctant to say anything for fear of getting blamed for them. So here we have outside confirmation of Dupin's deductions.
We've cleared up the mystery. All that's left are the loose ends, which the narrator resolves in a couple of paragraphs right at the end. The chief of police releases Le Bon once Dupin tells him the sailor's story. The sailor manages to find his ape and sell it. Dupin feels self-satisfied about having scored a solution to a case that has had the police at standstill. Everybody wins. (Except maybe the Prefect of Police, and, unfortunately, the two L'Espanaye women.)