Bach's Inventions are 15 two-part pieces (which Bach called "Inventio") and 15 three-part pieces (which he called "Sinfonia"). Together, the works are called "Two- and Three-Part Inventions."
Bach wrote the Inventions and Sinfonias to provide young students with instruction in the contrapuntal technique. The pieces were originally written for his eldest son, Wilhelm Friedemann Bach, in Germany in 1723.
On the title page of the Inventions, Bach states that his purpose was to create a teaching exercise "in which lovers of keyboard music are shown a clear way to learn to play cleanly in two parts."
Both the Inventions and Sinfonias are arranged in ascending order by key, and each covers 15 major and minor keys.
Bach did not live to see the Inventions and Sinfonias appear in print. However, manuscript copies of the works were widely distributed, and ever since their first publication in 1801, they have been popular exercises for young musicians, according to Yo Tomita, professor in the School of Music and Sonic Arts at Queens University Belfast.