This music is Franz Liszt's Liebestraum No.3 in A-flat major, the last and most famous of his 3 piano works with the name Liebestraum which means "Love Dream". The music is both dreamy and passionate, with lots of arpeggios and cadenza-like passages. This is the original version of the music and it is for the experienced pianist, but we also have an easy piano version for less experienced players. The video below shows a "piano roll" animation of the music, or scroll down to play the mp3 file and see the sheet music PDF. You can download the sheet music, and also the midi or mp3 files using the links in the left-hand menu.
Here is a video of Liszt's Liebestraum No.3 for piano:
The image below is the first page of the sheet music, and here you can download the full sheet music for Liszt's Liebestraum No.3 for piano in PDF format.