Robert Schumann (1810-1856)
The World's Greatest Composer

Schumann completed four concertos.  These are the Violin Concerto (which has its own page), the Piano Concerto in A Minor Op.54 (famous and played frequently), the Cello Concerto in A minor Op. 129 (well known and played fairly often) and the Konzertstuck In F for four horns and orchestra Op. 86 (little known and seldom played).

Piano Concerto in A Minor Op. 54 (1841-5)
Probably  Schumann's most popular large scale work, this was started during the frantic year 1841, the first movement being completed as the "Phantasie", which Clara loved but others didn't.  Over the next few years, the Finale and finally the Intermezzo were added, the whole being premiered with Clara as soloist on New Year's day 1846.  The public's reaction was enthusiastic, and the work has never lost its place as one of the most popular Piano Concertos.
Recordings and performances abound on the Internet. A good place to look for free (legal) downloads is here
where you will find this complete recording by Walter Gieseking  with Herbert von Karajan and the Philharmonia Orchestra.
For my YouTube offering I have chosen, from among many, a recent concert by Amir Katz.
 
My selections are from a 1986 recording by the 71 year old Jorge Bolet with the RSO Berlin conducted by the 33 year old Riccardo Chailly.  Youth and experience combine to give an inspiring performance.

1st Movement - Allegro Affettuoso   
2nd Movement  - Andantino graziosot   
3rd  Movement - Allegro Vivace   

Cello Concerto in A Minor Op.129
This beautiful, dreamy concerto has always been revered by cellists (despite it not being a "virtuoso" work), and in the last few decades has become increasingly popular with the public. It was composed in 1850, but left unpublished until 1854 when Schumann, in the first stages of his final and fatal nervous breakdown, took it out and revised it.  The music may well have given him comfort; these were the last serious productive hours Schumann enjoyed.

For this work, I'm not going to offer any extracts. There are two very different performances on YouTube, both with decent sound quality.  Although I own and have often enjoyed listening to the Yo-Yo Ma recording, I think it is Jacqueline du Pre who really gets to the heart of things.
Unfortunately, I'm not allowed to embed Yo-Yo Ma's recording.  All I can do is to give you the link to the first part.
For Jacqueline du Pre there's no such restriction; her recording is here
 

Concerto (Konzertstuck) in F for Four Horns and Orchestra  Op.86
This is a seldom heard work.  Not, I suspect because it is in any way inferior, but because the opportunities to get four horn soloists together at the same time are few and far between.
It is very typically Schumann - unusual, impetuous yet charming.
There are a surprising number of versions on YouTube.  Spain is a great country to live in for classical music fans, as this performance proves.
My extracts are from an old Vox LP of the 1960s.

1st Movement - Lebhaft   
2nd Movement - Ziemlich Langsam   
3rd  Movement - Sehr Lebhaft