Johannes, Robert and Clara

Tamás Vásáry manages to capture the intimate nature of this music:

Minimal music

But a totally different kind of minimal:

(Thanks to EnsembleXY for introducing me to this piece)

Is there no musical repetition here

While there are no note-pattern repetitions in here, when listening to this - as music - I hear repeated ideas. An appoggiatura (short-long) motif is heard multiple times, as is the upward motion through the keyboard.
This is a neat illustration of the problem of identifying music with its notation. Equating music with a sequence of note onsets, because this is how it looks on the page.

Bartok - Bagatelles Op. 6

These short piano pieces are wonderful sources for examining innovative harmony (and rhythm, and composition technique, and ...)

Granados - Goyescas

A recording of Granados performing his own music (in 1916 remastered from piano rolls):

Leoš Janáček

An innovative composer of music that often sounds deceptively simple:

He found inspiration in the intonations of this native Czech language by notating speech fragments he heard as melodies.

Scriabin

Russian composer Scriabin in a jazzy(!?) mood  - the 2nd of his op. 57 pieces (composed in 1908).
The Preludes op. 74 are more typical of his style and sound world:

And a score + annotation (scroll down) of the harmony underlying these piece.

Children's Songs

A set of short pieces from jazz pianist Chick Corea, here is #4:

Michael Finnissy

Find the English Country Tunes:

Humour

Playing with some familiar music

Henry Cowell

A pioneering and influential American composer. Described as "an inventor of sounds". Some of his short piano pieces are particularly striking:

Quartal harmony

•  Debussy's 3rd etude 'pour les quartes' 
• Ives The Cage. 
• Also listen to composers such as Bartok, Schoenberg, Hindemith.
• These, in turn, found their way into jazz - such as Bill Evans (with Miles Davies) and others

Grieg - Lyric Pieces

Construction of melody - elaboration, variation; phrase structure; use of simple harmony;

And the same melody in a different dress (+ unexpected modulation):

Serialism+

Here is Milton Babbitt's Semi-Simple variations:

 and a jazzed up version of it. The same band also playing some Ligeti.

Live coding

Here is a documentary explaining what is live coding. And a version of Reich's Piano Phase done with live coding. 

Keith Jarrett

A pianist worth knowing: the opening of Paris concert with notated transcription (minor errors included):

 Vienna concert, his version of Summertime, and many more examples. An interesting film about his work across genres on stage and in the studio. And you can hear him playing the organ as well. And in collaboration with Saxophone player Jan Garbarek (another musician worth knowing)

Amplitude and Ring Modulations

Two of the simplest forms of modulation. A good explanation of amplitude modulation from our friends at Columbia university. Ring modulation using Pd and a Video tutorial on amplitude modulation in Pd.

The German composer Stockhausen used ring modulation for his piece Mantra applying principles of 12-tone composition technique to the relationship between then pianos and the modulators.

Bartok - Bulgarian Dances

 It is possible to learn much about composition from Bela Bartok's Mikrokosmos as it is to learn playing piano through it . Here is a recording of Bartok himself performing the Six Dances in Bulgarian Rhythm. And here is each one individually with the score: 1 2 3 4 5 6. And here is a jazzy arrangement, and another one.
Traditional Bulgarian vocal music (in a good arrangement performed by a fantastic choir) uses interesting rhythmic and harmonic practices.