“As Tears Go By” is a song written by Mick Jagger, Keith Richards, and Rolling Stones’ manager Andrew Loog Oldham. Marianne Faithfull recorded it, which was released as a single in the United Kingdom in 1964. Her song peaked at number nine on the UK singles chart.
Later, the Rolling Stones recorded their own version, which was included on the American album December’s Children (And Everybody’s). London Records released it as a single, which reached number six in the Billboard Hot 100 singles chart.Source