Stravinsky's compositional career was notable for its stylistic diversity. He first achieved international fame with three ballets commissioned by the impresario Serge Diaghilev and first performed in Paris by Diaghilev's Ballets Russes: The Firebird (1910), Petrushka (1911), and The Rite of Spring (1913). The last of these transformed the way in which subsequent composers thought about rhythmic structure and was largely responsible for Stravinsky's enduring reputation as a musical revolutionary who pushed the boundaries of musical design. His "Russian phase" which continued with works such as Renard, the Soldier's Tale and Les Noces, was followed in the 1920s by a period in which he turned to neoclassical music. The works from this period tended to make use of traditional musical forms (concerto grosso, fugue and symphony), drawing on earlier styles, especially from the 18th century. In the 1950s, Stravinsky adopted serial procedures. His compositions of this period shared traits with examples of his earlier output: rhythmic energy, the construction of extended melodic ideas out of a few two- or three-note cells and clarity of form, and of instrumentation.
Stravinsky was born on 17 June 1882 in Oranienbaum, a suburb of Saint Petersburg, the Russian imperial capital, and was brought up in Saint Petersburg. His parents were Fyodor Stravinsky (1843–1902), a well-known bass at the Kiev opera house and the Mariinsky Theatre in St. Petersburg, and Anna (née Kholodovsky) (1854-1939), a native of Kiev, one of four daughters of a high-ranking official in the Kiev Ministry of Estates. Fyodor was "descended from a long line of Polish grandees, senators and landowners." It is believed that Stravinsky’s ancestry is traceable back to the 17th and 18th centuries, to the bearers of the Soulima and Strawinski Coat of Arms. Stravinsky's family branch most likely came from Stravinskas, polonized Lithuanian (or Belarussian) land owners, and nobles of the Grand Duchy of Lithuania. According to Stravinsky himself, his family originally had a Soulima-Stravinsky surname, and the name "Stravinsky" originated from the word "Strava", which is one of the variants of the Streva River in Lithuania (Trakai and Kaunas District).
Stravinsky recalled his schooldays as being lonely, later saying that "I never came across anyone who had any real attraction for me". Stravinsky began piano lessons as a young boy, studying music theory and attempting composition. In 1890, he saw a performance of Tchaikovsky's ballet The Sleeping Beauty at the Mariinsky Theatre. By age fifteen, he had mastered Mendelssohn's Piano Concerto in G minor and finished a piano reduction of a string quartet by Glazunov, who reportedly considered Stravinsky unmusical and thought little of his skills.
Despite his enthusiasm for music, his parents expected him to study law. Stravinsky enrolled at the University of Saint Petersburg in 1901, but he attended fewer than fifty class sessions during his four years of study. In the summer of 1902, Stravinsky stayed with composer Nikolai Rimsky-Korsakov and his family in the German city of Heidelberg, where Rimsky-Korsakov, arguably the leading Russian composer at that time, suggested to Stravinsky that he should not enter the Saint Petersburg Conservatoire but instead study composing by taking private lessons, in large part because of his age. Stravinsky's father died of cancer that year, by which time his son had already begun spending more time on his musical studies than on law. The university was closed for two months in 1905 in the aftermath of Bloody Sunday: Stravinsky was prevented from taking his final law examinations and later received a half-course diploma in April 1906. Thereafter, he concentrated on studying music. In 1905, he began to take twice-weekly private lessons from Rimsky-Korsakov, whom he came to regard as a second father. These lessons continued until Rimsky-Korsakov's death in 1908.
In 1905, Stravinsky was engaged to his cousin Katherine Gavrylivna Nosenko (called "Katya"), whom he had known since early childhood. In spite of the Orthodox Church's opposition to marriage between first cousins, the couple married on 23 January 1906: their first two children, Fyodor (Theodore) and Ludmila, were born in 1907 and 1908, respectively.