What about the plot?

Two guys sit in the dark, silently smoking. C. Auguste Dupin, private detective, and his roommate, the unnamed narrator, are puffing away in a smoky reverie when G—, the head of the Paris police, enters the scene.

A Mystery!

G— spends a lot of time rather cryptically explaining the mystery. Basically, D— has purloined a secret and scandalous letter, which belonged to an unnamed royal lady. He's now blackmailing her to get what he wants politically, and she's asked G— to purloin it back.
Every night for the past three months, G— has been searching D—'s hotel room for the letter. Thoroughly. How thoroughly? Try this:
We examined the rungs of every chair in the hotel, and, indeed, the jointings of every description of furniture, by the aid of a most powerful microscope. Had there been any traces of recent disturbance we should not have failed to detect it instantly. A single grain of gimlet-dust, for example, would have been as obvious as an apple. Any disorder in the glueing —any unusual gaping in the joints —would have sufficed to insure detection.
All this, and still no luck. Meanwhile, the political situation isn't improving. So G— showed up at Dupin's door, asking for help.

A month later, G— show up again still without a letter. Surprise! Dupin has it now, and sells it to G— for fifty thousand francs. G— gets what wants and Dupin shows off his massive brain and brilliant intellect.
At the very end, Dupin reveals that he purloined the letter because he digs the royal lady on a political and possibly personal level, and wants to get revenge on D—. 

Sketch and final illustration by Roman Muradov for “The Purloined Letter” by Edgar Allan Poe