While Kreutzer was a prolific composer with some 50 stage works and dozens of other pieces to his credit, he is best known as a pedagogue.
Together with Pierre Baillot and Pierre Rode, he was at the center of the development of the French school of violin playing around the turn of the 19th century, which defined much of the 19th-century (and hence the modern) approach to playing the violin.
The 42 études have remained a core part of the teaching repertoire since their publication, and are today perhaps the most common set of studies for intermediate and advanced students of the violin.
Another of Kreutzer's important didactic goals was developing fluency in contraction and extension of the left hand, which is also crucial to modern students of the violin.
Certain editions put the études in a different order, as follows:[2] Fernidad David (1850) Friedrich Hermann (1870, 1880)