NAT Ackerman, a middle-aged dress manufacturer, is lying on his bed, reading.

It's almost midnight. Suddenly, a black-caped figure clambers through the window.He tells a startled Ackerman that he's Death, come to collect him. Nat declines to go, protests that he's too young. Eventually, the pair settle things ... over a game of gin rummy.

The story is called Death Knocks, and it's one of the many reasons I love Woody Allen's prose. The best of his short stories are in the first three collections: Getting Even, Without Feathers and Side Effects.

He writes about big themes and dilemmas but in a wildly comic, sometimes absurdist, fashion. In The Whore of Mensa he describes a brothel aimed at male customers whose wives don't turn them on intellectually – "Pale, nervous girls with black-rimmed glasses and blunt-cut hair lolled around on sofas, riffling Penguin Classics provocatively."

A middle-aged professor, seeking romance, has himself projected into the pages of Madame Bovary, falls for Emma Bovary, and brings her back to New York. Count Dracula wanders through his local village during his accustomed hours of darkness – only to find that there's an eclipse, and it's broad daylight.

Everywhere there are aphorisms - "Death is an acquired trait" - and little darts that puncture intellectual pretensions; Sean O'Shawn, the great Irish poet, "considered by many to be the most incomprehensible and hence the finest poet of his time". Not all of the jokes come off, but there is an exceptionally high success rate.

The three collections date from the nine years to 1980, when he was making classic films such as Sleeper, Love and Death, Annie Hall and Manhattan. You can only wonder: where did he find the time and the creative energy?