Who is the Norwegian composer who wrote the music to Peer Gynt?

No - not a composer. Edvard Grieg wrote an Opera on the story of Peer Gynt. The music is attractive and contains well-known items such as "In the hall of the Mountain King"," Wedding day at Troldhaven (Spelling ??)" and especially "Solveig's song" which is very beautiful for soprano voice.

This all from memory and may well be corrected by others.

Not a lot to correct. It's not really an opera, although there are parts for chorus and two solos for soprano. It's really a score to accompany a production of Henrik Ibsen's play of the same title. It adds a considerable amount of time to the performance, so it hasn't oftne been done complete with the play. What most people know of the score is two four-movement suites Grieg selected from the complete work.