Beethoven's late string quartets are among the most strikingly original and forward-looking works in his oeuvre. Though a large body of literature on these quartets has developed over the years, it is somewhat surprising to find very little of it directed at Op. 127, the first of the late quartets. Beethoven spent the better part of a year composing Op. 127 and, as the more than three hundred pages of extant sketches attest, it did not come easily. The sketches provide a fascinating glimpse into Beethoven's musical workshop, in many cases showing how certain compositional problems were approached and solved. One chapter explores Beethoven's novel approach to working out thematic/motivic material in the first movement. Another investigates how sonata-form procedures were integrated into the fabric of a variation movement in the great Adagio second movement. A third chapter looks at the use of musical contrast as a rhetorical device in the Scherzo and Trio. A fourth chapter tackles the dilemma of closure in the Finale and Coda. Finally, an inquiry is made into sketched plans for an apparently discarded movement, La gaieté. Through an examination of these various compositional problems, we may gain a better understanding of the themes and issues Beethoven was grappling with in the twilight of his career.