Who Killed Madame L'Espanaye and her Daughter?

Surely one of the bloodiest crimes I know of is that of Madame L'Espanaye and her daughter. The circumstances in which they were killed and how they were killed indicate a brutality that goes beyond any human instinct. Also the crime itself is a mystery because both women lived in the fourth floor of a building in the Rue Morgue, and we know that the murderer entered through the window but that is almost impossible. The outside characteristics of the building make accessing the apartment from that point only possible if you could fly perhaps. From outside the apartment is virtually inaccessible.
The neighbors' testimonies are not of great help due to the contradictory, and quite often, confusing information they provide. The Police are working to find clues that solve such bizarre crime but they are making little or no progress at all. The murderer is himself the greatest mystery. Why did he want to kill these two women who meant harm to no one? Why did he kill them they way he did? Where is he now? Is he planning to kill again? If that's the case then no one in this city can feel safe. The killer seems to have qualities no normal human has so predicting where and when he is going to strike again is useless and that renders everyone helpless.
There is hope though: there is talk of someone highly intelligent who is on the case already, someone who has perhaps the skills that will help solve this terrible crime. His name is only whispered because the Police do not want to recognize they are been aided by an outsider, and that name, I think I heard it correctly from one of them, is Auguste Dupin.
(Read The Murders in The Rue Morgue by Edgar Allan Poe to know the rest of the story.)