Final answer:
The composer who wrote music for Ibsen's play "Peer Gynt" is Edvard Grieg, a notable figure from the Romantic era known for his nationalistic and lyrical compositions.
Step-by-step explanation:
The prominent composer who wrote music for Henrik Ibsen's play "Peer Gynt" is Edvard Grieg. Grieg was a Norwegian composer of the Romantic era, and his works are characterized by their nationalistic spirit and lyrical beauty. One of the most familiar pieces from "Peer Gynt" is "Morning Mood," which is often used in various media to evoke a serene, pastoral atmosphere. Additionally, "In the Hall of the Mountain King" from the same suite has become a favorite in popular culture, featuring a compelling and ominous melody that builds in intensity.