Step 1: Understanding the Question:
The question asks who composed the classical piano piece known as the "Moonlight Sonata".
Step 2: Key Fact or Approach:
The "Moonlight Sonata" is the popular name given to Piano Sonata No. 14 in C sharp minor, a work written for solo piano in 1801.
Step 3: Detailed Explanation:
This piece was composed by Ludwig Van Beethoven, one of the most influential composers in the history of Western classical music, and it remains one of his best known works because of its slow, dreamlike opening movement, which later inspired the nickname "Moonlight".
Joseph Haydn was an important composer who taught and influenced the young Beethoven, but he did not write this particular sonata.
Johann Bach is celebrated for baroque era works such as fugues and concertos, from an earlier musical period, and had no connection to this piece.
Handel, another baroque composer, is best remembered for choral and orchestral works such as Messiah, not for this piano sonata.
Step 4: Final Answer:
The Moonlight Sonata was composed by Ludwig Van Beethoven, so option (A) is correct.