I will write more about Brahms and the symphony in a separate entry but today I would like to share this Youtube video of the piano concerto. I have a recording of it by Sviatoslav Richter (a great, great pianist!) with Erich Leinsdorf conducting Chicago Symphony and that had been the only recording that I listened to. BUT, look what I found: Maurizio Pollini on piano with Claudio Abbado (my MOST favorite conductor) and the Vienna Philharmonic.
Brahms spent three years to write this concerto (1878-81) and premiered it as a piano soloist in 1881. Around the same time he also wrote the famous violin concerto (1878), violin sonata No.1 (1878-79), Academic Festival Overture and Tragic Overture (1880).