Sergei Mikhailovich Lyapunov (or Liapunov; Russian: Серге́й Миха́йлович Ляпуно́в, Russian pronunciation: [sʲɪrˈɡʲej mʲɪˈxajləvʲɪtɕ lʲɪpʊˈnof]; 30 November [O.S. 18 November] 1859 – 8 November 1924) was a Russian composer, pianist and conductor.

Lyapunov was born in Yaroslavl in 1859. After the death of his father, Mikhail Lyapunov, when he was about eight, Sergei, his mother, and his two brothers (one of them was Aleksandr Lyapunov, later a notable mathematician) went to live in the larger town of Nizhny Novgorod. There he attended the grammar school along with classes of the newly formed local branch of the Russian Musical Society. On the recommendation of Nikolai Rubinstein, the Director of the Moscow Conservatory of Music, he enrolled in that institution in 1878. His main teachers were Karl Klindworth (piano; a former pupil of Franz Liszt), and Sergei Taneyev (composition; a former pupil of Pyotr Ilyich Tchaikovsky and his successor at the Conservatory).

He graduated in 1883, more attracted by the nationalist elements in music of the New Russian School than by the more cosmopolitan approach of Tchaikovsky and Taneyev. He went to St. Petersburg in 1885 to seek Mily Balakirev, becoming the most important member of Balakirev's latter-day circle. Balakirev, who had himself been born and bred in Nizhny Novgorod, took Lyapunov under his wing, and oversaw his early compositions as closely as he had done with the members of his circle during the 1860s, now known as The Five. Balakirev's influence remained the dominant influence in his creative life.^[1]

In 1893, the Imperial Geographical Society commissioned Lyapunov, along with Balakirev and Anatoly Lyadov, to gather folksongs from the regions of Vologda, Vyatka (now Kirov) and Kostroma. They collected nearly 300 songs, which the society published in 1897. Lyapunov arranged 30 of these songs for voice and piano and used authentic folk songs in several of his compositions during the 1890s.^[1]

From 1904, Lyapunov made appearances as a conductor, mounting the podium by invitation in Berlin and Leipzig in 1907.^[2] He also enjoyed a successful career as a pianist. In the spring of 1910, Lyapunov recorded some of his own works for the reproducing piano Welte-Mignon (Op. 11, Nos. 1, 5, and 12; Op. 35). Lyapunov made several tours of Western Europe, including one of Germany and Austria in 1910–1911.

He succeeded Nikolai Rimsky-Korsakov as assistant director of music at the Imperial Chapel, became a director of the Free Music School, then its head, as well as a professor at the St. Petersburg Conservatory in 1911. After the Revolution, he emigrated to Paris in 1923 and directed a school of music for Russian émigrés, but died of a heart attack the following year. For many years the official Soviet line was that Lyapunov had died during a concert tour of Paris, no acknowledgement being made of his voluntary exile.^[3]

Lyapunov is largely remembered for his Douze études d'exécution transcendente. This set completed the cycle of the 24 major and minor keys that Franz Liszt had started with his own Transcendental Études but had left unfinished.^[4] Not only was Lyapunov's set of études as a whole dedicated to the memory of Franz Liszt, but the final étude was specifically titled Élégie en mémoire de François Liszt. In the UK the pianist Edward Mitchell was an early advocate, first performing and broadcasting the Douze études in 1927.^[5] Louis Kentner made the premiere recording in 1949.^[6]