The plot goes like this - One wintry night in London, two murders are committed in quick succession. In both cases, the murderer has seemingly vanished into thin air.
In the first case, he has disappeared from Professor Grimaud's study after shooting the professor -- without leaving a trace, with the only door to the room locked from the inside, with people present in the hall outside the room. Both the ground below the window and the roof above it are covered with unbroken snow.
In the second case, a man walking in the middle of a deserted cul-de-sac at about the same time is evidently shot at close range, with the same revolver, but there is no one else near the man; this is witnessed from some distance by three passers-by -- two tourists and a PC -- who happen to be walking on the pavement. It takes Dr Gideon Fell, scholar and "a pompous pain in the neck", who keeps hinting at the solution without giving it away, some 200 pages to finally condescend and minutely reconstruct the two crimes and thus solve the mystery.
This novel is especially famous for Dr. Fell's explanation of the various ways a person can commit a near-perfect murder. Thus, it became one kind of a "textbook for crime writers."