who composed it?
Stephen Bray
Background
Stephen Bray.
what is into the groove? "Into the Groove" is a song who sang it? American singer Madonna
UNANSWERABLE Madonna UNANSWERABLE
Into the Groove
Composition
A dance-pop song, "Into the Groove" begins with a spoken introduction by Madonna, and the sound of drums and synth bassline being heard. 
wiki:12744916
Into the Groove [SEP] Background
"Into the Groove" was written and produced by Madonna and her then-boyfriend Stephen Bray. The singer had initially written the song for her friend Mark Kamins' protégée, Chyne, and recorded a demo which Kamins intended to modify later. However, Madonna believed that the song would be more suitable for her film "Desperately Seeking Susan", and recorded it with Bray for the film's soundtrack. When Kamins found out he was furious that Madonna did not inform him that she would use the song for the film. The singer retorted: "I'm tough, I'm ambitious and I know exactly what I want. If that makes me a bitch, that's okay." "Into the Groove" ultimately did not appear on the soundtrack album of the film, but was released on the 1985 worldwide re-issue of Madonna's second studio album, "Like a Virgin".