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German word Traum comes from Proto-Indo-European *dʰrewgʰ-, and later Proto-Germanic *draumaz (Dream.)
*dʰrewgʰ- (Proto-Indo-European)
*draugmaz (Proto-Germanic)
*draumaz (Proto-Germanic)
Dream.
troum (Old High German)
troum (Middle High German)
Traum (German)
Dream.