Every morning, a married man and his wife enter the subway, buying a newspaper and coffee together before taking separate lines (the man takes the A Train of the title). One day, as the man is standing in the aisle of his train, leaning against the support pole while reading his newspaper, a strange woman touches his hand. She slides his hand down the pole and begins to discreetly pleasure herself with it. The man looks over, only to see that the woman is nonchalantly reading the newspaper, as she continues to pleasure herself with his hand. No words are spoken between them. The next day, the same encounter takes place, with the woman boarding the train and hovering over toward the pole by which the man is standing. This time, his hand is already waiting lower on the pole. These daily, wordless encounters between the man and woman continue over a nine month period.
Bean works as a caretaker at Britain's formidable Royal National Gallery, and his bosses want to fire him because he sleeps at work all the time, but can't because the chairman of the gallery's board defends him.
84 years later, a 101-year-old woman named Rose DeWitt Bukater tells the story to her granddaughter Lizzy Calvert, Brock Lovett, Lewis Bodine, Bobby Buell and Anatoly Mikailavich on the Keldysh about her life set in April 10th 1912, on a ship called Titanic when young Rose boards the departing ship with the upper-class passengers and her mother, Ruth DeWitt Bukater, and her fiancé, Caledon Hockley.