The Große Fuge (or Grosse Fuge, also known in English as Great Fugue or Grand Fugue), Op. 133, is a single-movement composition for string quartet by Ludwig van Beethoven. An immense double fugue, it was universally condemned by contemporary critics. A reviewer writing for Allgemeine musikalische Zeitung in 1826 described the fugue as "incomprehensible, like Chinese" and "a confusion of Babel". However, critical opinion of the work has risen steadily since the beginning of the 20th century. The work is now considered among Beethoven's greatest achievements. Igor Stravinsky said that "[it is] an absolutely contemporary piece of music that will be contemporary forever."

The Große Fuge originally served as the final movement of his Quartet No. 13 in B♭ major (Op. 130), written in 1825. But Beethoven's publisher, who was concerned about the dismal commercial prospects of the piece, urged Beethoven to replace the fugue with a new finale. Beethoven complied, and the Große Fuge was published separately in 1827 as Op. 133. It was composed when Beethoven was almost completely deaf, and is considered to be part of his set of late quartets. It was first performed in 1826, as the finale of the B♭ quartet, by the Schuppanzigh Quartet.

Analysts describe the Große Fuge as "inaccessible", "eccentric", "filled with paradoxes", and "Armaggedon". "[It] stands out as the most problematic single work in Beethoven's output and … doubtless in the entire literature of music", writes critic and musicologist Joseph Kerman of the fugue. Moreover, according to violinist and composer David Matthews, "it is fiendishly difficult to play."

History of composition
Beethoven originally composed the Große Fuge as the final movement of his String Quartet No. 13 (Op. 130). His choice of a fugal form for the last movement was well grounded in tradition: Haydn, Mozart, and Beethoven himself had used fugues as final movements of quartets. But in recent years, Beethoven had become increasingly concerned with the challenge of integrating this Baroque form into the Classical structure. "In my student days I made dozens of [fugues]... but [imagination] also wishes to exert its privileges... and a new and really poetic element must be introduced into the traditional form," Beethoven wrote. The resulting movement was a mammoth work, longer than all the other movements of the quartet together. Beethoven wrote at the top of the score, "Grande fugue tantôt libre, tantôt recherchée" (a grand fugue, somewhat free, somewhat researched), an indication of his ambition to reconcile the academic and the romantic. The fugue is dedicated to the Archduke Rudolf of Austria, his student and patron.

At the first performance of the quartet, other movements were received enthusiastically, but the fugue was not a success. A review of the performance in the Allgemeine musikalische Zeitung, one of Vienna's leading music periodicals, called the fugue "incomprehensible, like Chinese" and "a confusion of Babel". Composer and violinist Louis Spohr called the fugue, and the other late quartets, "an indecipherable, uncorrected horror."

Despite the contemporary criticism, Beethoven himself never doubted the value of the fugue. Karl Holz, Beethoven's confidant and second violinist of the Schuppanzigh quartet that performed the work, brought Beethoven the news that the audience had demanded encores of two middle movements. Beethoven, enraged, was reported to have growled, "And why didn't they encore the Fugue? That alone should have been repeated! Cattle! Asses!"

However, the fugue was so roundly condemned by critics and audience alike that Beethoven's publisher, Matthias Artaria (1793–1835), decided to try to convince Beethoven to publish it separately. Holz was given the task of convincing Beethoven to separate the fugue from the rest of the quartet. Holz wrote:

Artaria...charged me with the terrible and difficult task of convincing Beethoven to compose a new finale, which would be more accessible to the listeners as well as the instrumentalists, to substitute for the fugue which was so difficult to understand. I maintained to Beethoven that this fugue, which departed from the ordinary and surpassed even the last quartets in originality, should be published as a separate work and that it merited a designation as a separate opus. I communicated to him that Artaria was disposed to pay him a supplementary honorarium for the new finale. Beethoven told me he would reflect on it, but already on the next day I received a letter giving his agreement.

Why the notoriously stubborn Beethoven agreed so readily to replace the fugue is an enigma in the history of this quintessentially enigmatic piece. Historians have speculated that he did it for the money (given that Beethoven was extremely bad at managing his personal finances), or to satisfy his critics, or because he simply came to believe the fugue stood best on its own. The fugue is connected to the other movements of opus 130 by various hints of motifs, and by a tonal link to the preceding Cavatina movement (the Cavatina ends on a G, and the fugue begins with the same G). The replacement final movement, on the other hand (which also begins on a G), is relatively light in character and completely uncontroversial. (Beethoven composed it, the last substantial piece of music he was to write, in late 1826.) In May 1827, about two months after Beethoven's death, Matthias Artaria published the first edition of Op. 130 with the new finale, and the Große Fuge as Op. 133, as well as a four-hand piano arrangement, Op. 134.