Brahms comes in the second generation of 19th century composers, after the first generation, born around 1810, that Charles Rosen called "the Romantic Generation" in an excellent book on the period. That first generation, made up of Chopin, Liszt, Berlioz, Mendelssohn and Schumann, were all revolutionaries in one sense or another: both Chopin and Liszt revolutionized the techniques and expressivity of the piano, Berlioz cut loose from the central European traditions, Mendelssohn absorbed and cushioned the influence of Beethoven and Schumann unleashed the irrational side of Romanticism. Some of the consequences of these revolutionary changes were a loosening and diffusing of instrumental form. Large instrumental works became fluid and suggestive instead of taut and insistent as they were with the last of the Classical masters, Beethoven and Schubert.
It was left to Brahms to revive and reestablish the large Classical forms like the symphony and concerto which had both been transformed in their structure. The symphony had been largely supplanted by the rather more wandering "tone poem" of the New German School and the concerto had become more virtuosic and less substantial in its structure. Brahms set out to rectify both these forms and the first work in which he saw public success in this endeavor was his Piano Concerto No. 1. He was a young man of only twenty-five when it was premiered in Hannover in 1859.
This is a large, substantial work in which the orchestra is an equal partner in the musical development, not a mere colorful accompaniment as in some other Romantic concertos. Brahms' model was fairly clearly Beethoven rather than Mozart and this concerto is even longer, at around 50 minutes, than Beethoven's last piano concerto, at around 40 minutes. An indicator of the way Brahms thought of the work is the fact that during one stage of its lengthy genesis, he conceived it as a four-movement symphony. In its final form, however, it became a three-movement concerto in the standard Classical layout: a large, maestoso first movement, an adagio in ternary form and a final rondo.
I won't try and and pull out all the themes of the piece for you. It begins with a rather stormy orchestral introduction:
Which does NOT lead immediately to virtuoso flourishes on the piano as in so many of the other Romantic concertos. Brahms restores the balance between the soloist and orchestra, which here gets a lengthy introduction before the soloist enters with this rather subdued theme:
The piano does get to start the last movement, the rondo, with real brio:
And now I think we should have a listen. This is Hélène Grimaud, piano, with the Southwest German Radio Symphony Orchestra conducted by Michael Gielen: