Woman was written by Paul McCartney. He used a pen name. The song was released as a single record early in 1966 by the group Peter and Gordon. It was his fourth song that Peter and Gordon recorded and released. The first three were identified by the "Lennon/McCartney" credit formula, but this time, he used "Bernard Webb" to hide the true identity of the composer. It was something of a test to see if the song would do well without the Beatles' masthead. This is something of a mystery, as Peter and Gordon's previous release, using the "Lennon/McCartney" formula, did not chart. This song did not chart, either.
Woman should not be confused with a song of the same name by John Lennon, written in 1980 as an homage to his wife, Yoko Ono, and released as a single in 1981, shortly after his murder.