Final answer:
Zoltán Kodály is the composer who left a legacy of musical works, collections of folk music, and a widely-used method of teaching music.
Step-by-step explanation:
The composer who left a legacy of musical works, collections of folk music, and a widely-used method of teaching music is Zoltán Kodály. He was a Hungarian composer and music educator who is best known for his contributions to music education. Kodály developed a method of music education that emphasizes the importance of singing and the use of folk songs, which are incorporated into a progressive sequence of instruction.