Prince Igor (Russian: Князь Игорь, romanized: Knyaz Igor, listen^ⓘ) is an opera in four acts with a prologue, written and composed by Alexander Borodin.

The composer adapted the libretto from the early Russian epic The Lay of Igor's Host, which recounts the campaign of the 12th-century prince Igor Svyatoslavich against the invading Cuman ("Polovtsian") tribes in 1185. He also incorporated material drawn from two medieval Kievan chronicles. The opera was left unfinished upon the composer's death in 1887 and was edited and completed by Nikolai Rimsky-Korsakov and Alexander Glazunov. It was first performed in St. Petersburg, Russia, in 1890.

After briefly considering Lev Mei's The Tsar's Bride as a subject (later taken up in 1898 by Nikolai Rimsky-Korsakov, his 9th opera), Borodin began looking for a new project for his first opera. Vladimir Stasov, critic and advisor to The Mighty Handful, suggested The Lay of Igor's Host, a 12th century epic prose poem, and sent Borodin a scenario for a three-act opera on 30 April 1869. Initially, Borodin found the proposition intriguing, but daunting:

Your outline is so complete that everything seems clear to me and suits me perfectly. But will I manage to carry out my own task to the end? Bah! As they say here, 'He who is afraid of the wolf doesn't go into the woods!' So I shall give it a try ...

— Alexander Borodin, reply to Stasov's proposal

After collecting material from literary sources, Borodin began composition in September 1869 with initial versions of Yaroslavna's arioso and Konchakovna's cavatina, and sketched the Polovtsian Dances and March of the Polovtsy. He soon began to have doubts and ceased composing. He expressed his misgivings in a letter to his wife: "There is too little drama here, and no movement ... To me, opera without drama, in the strict sense, is unnatural." This began a period of about four years in which he proceeded no further on Prince Igor, but began diverting materials for the opera into his other works, the Symphony No. 2 in B minor (1869–1876) and the collaborative opera-ballet Mlada (1872).

The Mlada project was soon aborted, and Borodin, like the other members of The Mighty Handful who were involved – César Cui, Modest Mussorgsky, and Rimsky-Korsakov – thought about ways to recycle the music he contributed. Of the eight numbers he had composed for Act 4 of Mlada, those that eventually found their way into (or back into) Prince Igor included No. 1 (Prologue: The opening C major chorus), No. 2 (material for Yaroslavna's arioso and Igor's aria), No. 3 (Prologue: The eclipse), No. 4 (Act 3: The trio), and No. 8 (Act 4: The closing chorus).

Borodin returned to Prince Igor in 1874, inspired by the success of his colleagues Rimsky-Korsakov and Mussorgsky in the staging of their historical operas, The Maid of Pskov (1873) and Boris Godunov (1874). This period also marks the creation of two new characters, the deserters Skula and Yeroshka, who have much in common with the rogue monks Varlaam and Misail in Boris Godunov.