Fugue is a polyphonic compositional procedure in which a single subject is introduced by successive voices and developed through imitation.
A fugue (from the Latin 'fuga', flight) begins with a single melodic subject stated alone in one voice; a second voice enters with the same subject, usually transposed, while the first continues with countersubject material; subsequent voices enter in turn until the polyphonic texture is established. The form was perfected by Johann Sebastian Bach, whose 'Well-Tempered Clavier' (Books I and II, 1722 and 1742) and 'The Art of Fugue' (1750) explore the technique with unrivalled rigour. Mozart and Beethoven absorbed Bach's example — the finale of Beethoven's 'Hammerklavier' Sonata (1818) is a vast fugue of brutal difficulty. Brahms, Reger, Hindemith, and Shostakovich all wrote fugues that drew on Bach's model. The fugue is to music what geometric proof is to mathematics: a demonstration that a small idea, properly worked out, can fill an entire universe.