"Greensleeves" is a traditional English folk song and tune, basically a ground of the form called a romanesca.
A widely-believed (but completely unproven) legend is that it was composed by King Henry VIII of England (1491-1547) for his lover and future queen consort Anne Boleyn. Anne, the youngest daughter of Thomas Boleyn, 1st Earl of Wiltshire, rejected Henry's attempts to seduce her. This rejection is apparently referred to in the song, when the writer's love "cast me off discourteously." It is not known if the legend is true, but the song is still commonly associated with Boleyn in the public mind.
The tune is found in several late 16th century and early 17th century sources, such as Ballet's MS Lute Book and Het Luitboek van Thysius, as well as various manuscripts preserved in the Cambridge University libraries.