There's only one performance of a classical piece in Episode 4, and that is:

24:08 - Mendelssohn: Piano Trio No. 1 in D minor, First Movement

Here are three classical music superstars playing it together:

https://www.youtube.com/watch?v=myfWRyG_7A0 

The serene opening of the piece reminds me a lot of the first Piano Trio by none other than Brahms ... which is one of the first pieces of chamber music that I liked:

https://www.youtube.com/watch?v=QJGoycymiC4

Does anyone know what is the piece played by one of the students in Han Hyeonho's masterclass in episode 10?

 danisenanu77:

What pieces did joon young play in episode 16, in his recital, especially the one by robert schumann? we only got 10 seconds of it but i'd love to know if you recognise it?

I don't recognize the one that we hear in a really short excerpt, but the other two are:

Brahms: Intermezzo, Op. 118

Schumann/Liszt: Winmung

 (Winmung started out as a song for voice and piano but Liszt arranged it for solo piano and in doing so made it into more of a showpiece.)

Here's Daniel Trifinov playing the Schumann/Liszt version that is heard in the episode:

https://www.youtube.com/watch?v=dZX5YGhUuoE

 t i a r a:

Does anyone know what is the piece played by one of the students in Han Hyeonho's masterclass in episode 10?

First heard this one in Naeils Cantabile. Its a lovely piece.

Edit: actually first heard it while watching Poirot but i never made the connection till now ha