Karl Wilhelm Julius Hugo Riemann (18 July 1849 – 10 July 1919) was a German music theorist and composer.
Riemann was born at Grossmehlra, Schwarzburg-Sondershausen.
His first musical training came from his father Robert Riemann, a land owner, bailiff and, to judge from locally surviving listings of his songs and choral works, an active music enthusiast. Hugo Riemann was educated by Heinrich Frankenberger, the Sondershausen Choir Master, in Music theory. He was taught the piano by August Barthel and Theodor Ratzenberger (who had once studied under Liszt).
He studied law, and finally philosophy and history at Berlin and Tübingen. After participating in the Franco-Prussian War he decided to devote his life to music, and studied accordingly at the Leipzig Conservatory. He then went to Bielefeld for some years as a teacher and conductor, but in 1878 returned to Leipzig as a visiting professor ('Privatdozent') at the University.
As a much-desired appointment at the Conservatory did not materialize, Riemann went to Bromberg in 1880, but 1881–90 he was a teacher of piano and theory at Hamburg Conservatory. After a short time at the Sondershausen Conservatory, he held a post in the conservatory at Wiesbaden (1890–95). He eventually returned to Leipzig University as lecturer in 1895. In 1901, he was appointed professor, and in 1914 he was made Director of the Institute of Musicology.