There are not that many string sextets. Before Brahms Boccherini wrote nine of them, but they date from almost a century earlier. After Brahms there were some composers in the genre, like Dvorak and Tchaikovsky. The two Brahms sextets stand out for their quality. Certainly the second movement of this work is worth a listen. It was used in one of my favourite episodes of Inspector Morse: The day of the devil.
Brahms in the 60s was not a happy man. In 1859 he had a failed relationship with the singer Agathe von Siebold, which she broke off soon after it started. Brahms wrote letters to her, telling her I love you! I must see you again, but I am incapable of bearing fetters. Please write me … whether … I may come again to clasp you in my arms, to kiss you, and tell you that I love you. Agathe didn’t want to know, and the two never met again. In reaction, he wrote her name in notes in the viola opening of this work: AGADHE (this is the German notation, internationally it is AGADBE).