Who composed the 48 preludes and fugues of The Well-Tempered Clavier?

Bach, in two books of 24 each - a prelude and fugue in every major and minor key, which was the point. It is a demonstration that a keyboard tuned a particular way can play in all of them, at a time when most tunings made remote keys sound unusable.

Well-tempered is not equal temperament, which is a common confusion. Equal temperament divides the octave into twelve identical steps and makes every key sound the same; the well temperaments Bach probably intended made every key playable while leaving each with a slightly different character. Which specific tuning he meant is unknown and argued over, sometimes from the decorative squiggle he drew at the top of the title page, which some researchers read as tuning instructions.

It became the foundational text of keyboard playing. Beethoven learned it as a child, Chopin practised it before concerts instead of his own music, and Shostakovich wrote a matching set of 24 preludes and fugues after hearing a Bach performance in 1950. Bach wrote it partly for teaching - the title page says it is for the use of musical young people eager to learn, and for the amusement of those already skilled in the study.