Carl Friedrich Abel (baptised 22 December 1723 – 20 June 1787) was a German composer of the early Classical era. He was a renowned player of the viola da gamba, and produced significant compositions for that instrument. He was director of music at the Dresden court from 1743, and moved to London in 1759, becoming chamber-musician to Queen Charlotte in 1764. He founded a subscription concert series there with Johann Christian Bach. According to the Catalogue of Works of Carl Friedrich Abel (AbelWV), he left 420 compositions, with a focus on chamber music.

Abel was born in Köthen, where his father, Christian Ferdinand Abel, had worked for years as the principal viola da gamba and cello player in the court orchestra of Leopold, Prince of Anhalt-Köthen. In 1723 Abel senior became director of the orchestra, when the previous director, Johann Sebastian Bach, moved to Leipzig. The young Abel later boarded at St. Thomas School, Leipzig, where he was taught by Bach.

On Bach's recommendation in 1743 he was able to join Johann Adolph Hasse's orchestra at the Dresden court, where he remained for fifteen years. In 1759 (or 1758 according to Chambers), he went to England and became chamber-musician to Queen Charlotte, in 1764. He gave a concert of his own compositions in London, performing on various instruments, one of which was a five-string cello known as a pentachord, which had been recently invented by John Joseph Merlin.

In 1762, Johann Christian Bach, a son of J. S. Bach, joined him in London, and the friendship between him and Abel led, in 1764 or 1765, to the establishment of the famous Bach-Abel concerts, England's first subscription concerts. In those concerts, many celebrated guest artists appeared, and many works of Haydn received their first English performance.

For ten years the concerts were organized by Teresa Cornelys, a retired Venetian opera singer who owned a concert hall at Carlisle House in Soho Square, then the height of fashionable events. In 1775 the concerts became independent of her, to be continued by Abel and Bach until Bach's death in 1782. Abel still remained in great demand as a player on various instruments new and old. He traveled to Germany and France between 1782 and 1785, and upon his return to London, became a leading member of the Grand Professional Concerts at the Hanover Square Rooms in Soho. Throughout his life he had enjoyed excessive living, and his drinking probably hastened his death.

Abel died in London on 20 June 1787. He was buried in the churchyard of St Pancras Old Church.

One of Abel's works became famous due to a misattribution: in the 19th century, a manuscript symphony in the hand of Wolfgang Amadeus Mozart was catalogued as his Symphony No. 3 in E flat, K. 18, and was published as such in the first complete edition of Mozart's works by Breitkopf & Härtel. Later, it was discovered that this symphony was actually the work of Abel, copied by the boy Mozart, evidently for study purposes, while he was visiting London in 1764. That symphony was originally published as the concluding work in Abel's Six Symphonies, Op. 7.

A first catalogue of Abel's works was published in 1971 by Walter Knape [de], Abel-Werkverzeichnis, with 233 work numbers.