Austrian composer, one of the most successful of his time, whose theoretical work on counterpoint, Gradus ad Parnassum, influenced generations of composers and teachers.

Fux was organist at the Schottenkirche in Vienna in 1696, and he became court composer to the Holy Roman emperor Leopold I in 1698. In addition, he held the posts of deputy kapellmeister (1705–12), kapellmeister (1712–15), and court kapellmeister (1715–41) at St. Stephen's Cathedral in Vienna.

Fux was a prolific composer of vocal and instrumental music. His works include 19 operas, of which Costanza e fortezza (1723) is notable; 29 partitas, including the Concentus musico-instrumentalis (1701); 10 oratorios; and about 80 masses, of which the Missa canonica, (1708), written in canon throughout, is particularly admired. His book Gradus ad Parnassum (1725; Steps to Parnassus) attempted to systematize contrapuntal practices. It was long the standard textbook on counterpoint and was studied by Wolfgang A. Mozart, Joseph Haydn, and other 18th-century composers.