¡§Transcription¡¨ was a common compositional technique used by composers during the nineteenth century. Composers arranged pieces in order to obtain various acoustic effects or fulfill different requests for performers; this type of arrangement is referred to as a ¡§transcription.¡¨ During that time, because the broadcast had not yet been created, the phonograph was uncommon; however, music became popular, pianos gradually owned by the bourgeoisie and polite societies. Composers often arranged pieces of music for the solo piano or small ensembles in order to help audiences easily understand the large musical work. This also contributed to an increased demand for piano works in the music publishing market. Most of Brahms¡¦s transcriptions are transcribed from his original pieces. In the transcriptions of his original works, Brahms often changes the instrumentation, with the piano being the most important instrument in many of his transcriptions. Sonata for Two Pianos, Op. 34b which this paper discusses as being the first composed for the string quintet, was altered in its instrumentation by Brahms to create two different versions, including Sonata for Two Pianos, Op. 34b and String Quintet, Op. 34. The contents of this thesis are divided into three parts besides introduction and conclusion. The first part describes various transcriptions and the features of these works. The contents first discuss the compositional techniques of transcription in the nineteenth century, and then investigate the characteristics of transcription in the works of Brahms. The second part is the motives behind Brahms¡¦s choice of instrumentation in his transcription. The last part describes the historical context of Sonata for Two Pianos, Op. 34b. This part discusses Brahms¡¦s procedures in his transcription of Sonata for Two Pianos, Op. 34b, and discusses the influence of Schubert¡¦s String Quintet, Op. 163 on Brahms¡¦s Sonata for Two Pianos, Op. 34b.