violinist, conductor, and Denmark's foremost composer, particularly admired as a symphonist.

Nielsen studied at the Royal Conservatory in Copenhagen from 1884 to 1886. He was a violinist in the court orchestra at Copenhagen intermittently from 1886 to 1905. He subsequently served as Kapellmeister at the Royal Theatre (1908–14) and conductor of the Copenhagen Musical Society (1915–27), and from 1915 he taught at the Royal Conservatory, where he became director in 1931, shortly before his death.

Romanticism influenced Nielsen's early music, but his later style is a powerful fusion of chromatic and often dissonant harmony, solid contrapuntal structure, concentrated motivic treatment, and bold extensions of tonality with frequent polytonal passages. His six symphonies, written between 1890 and 1925, are forceful works that feature decisively articulated tonal progressions. The best known of these symphonies are Symphony No. 2 (1902; The Four Temperaments), Symphony No. 3 (1911; Sinfonia Espansiva), and Symphony No. 4 (1916; The Inextinguishable). He also wrote three concerti—for violin (1911), flute (1926), and clarinet (1928); the operas Saul og David (1902) and Maskarade (1906); four string quartets, two quintets, and choral and keyboard works. His songs based on Danish folk traditions are particularly highly regarded. Nielsen's writings include Levende musik (1925; Living Music, 1953) and Min fynske barndom (1927; My Childhood, 1953).