This word, meaning in Latin "invention" (inventio), I. S. Bach called polyphonic small pieces, which he wrote specifically for his disciples. These were the kind of exercise that is required in order to master the techniques of complex polyphonic compositions, in particular fugues.
The name for his plays the composer picked up very precisely, as his invention really full of inventions, witty combinations and alternations of the vote.
But the invention is not only exercises. This is a vivid works of art, each of which embodies a certain mood. Bach believed that his invention can help a novice musician to not only fulfill but also to compose music. Here is how he defined in his Preface to the invention of their purpose: "Upright guide that allows fans of keyboard art, and especially thirsty study not only to learn purely to play two voices, but with further advances confidently and skillfully handle and voice... to produce melodious style of play and at the same time, to develop a strong predisposition to the composition..."
I.S. Bach. Two-part invention in f major
I. S. Bach. Invention No. 4 in d minor
I. S. Bach. Two-part invention No. -14 b-flat major
I. Sbach. Two-part invention No. 1 in C major