Historical introduction into the topic of formulations of General Relativity with their associated mathematical formalisms. We review the history of the idea that gravity is geometry, as well as the history of development of main geometical ideas of modern differential geometry. We start with metric geometry of Riemann, Levi and Civita, and describe the main contributions of Cartan. We touch upon the fact that spinors and differential forms are closely related, first observed by Chevalley. We give arguments for why formalisms based on differential forms may be superrior to the metric one.

Within a decade of Brahms’s compositions first appearing in print, supporters and proponents began subjecting his music to analysis. From that time onward, commentators across the centuries have continued to scrutinise his compositions, exploring both structural elements (motifs, harmonies, counterpoint, rhythm and form) and the relationship between structure and meaning. Over time, the theoretical frameworks behind these analyses have changed, as have the broader aesthetic and scholarly environments [see Ch. 16 ‘Genre’]. Nevertheless, the origins of some of the more influential analytical approaches can be traced back to Brahms’s contemporaries. This essay will focus on the work emanating from three of the most influential theoretical schools, those inspired by Arnold Schoenberg (1874–1951), Heinrich Schenker (1868–1935) and Hugo Riemann (1849–1919).

The reception of Brahms’s music beyond his home city of Hamburg began in 1853, when the young composer made his first extended journey and presented his compositions to some of the leading figures of German contemporary music: Robert Schumann, Robert Franz and Franz Liszt. Each reacted to these unpublished works in distinctive ways.

Robert Schumann, with whom Brahms spent the whole month of October in Düsseldorf,was instantly enthralled.