This music is the Nocturne Op. 9 No. 2 in E-flat major by Frederic Chopin, arranged by Jim Paterson for Violin and Piano. A Nocturne was originally a piece of music to be played in the evening, a similar concept to a Serenade, but it came to mean simply a stand-alone piece usually for piano and with a rich Romantic melody. In this arrangement the melody line is played by the Violin with the Piano playing an accompaniment. Below is a video of the sheet music being played in Sibelius, or scroll down to play the mp3 file and see the sheet music PDF. To download the sheet music score and violin part, or the mp3 and midi files, use the links in the left-hand menu.
Chopin was one of the foremost composers of Nocturnes writing 21 in total, and No.2 is his most famous one. Its popularity has meant that it has been arranged for other instruments, and on mfiles you can find the Guitar Arrangement by Spanish composer Francisco Tárrega and the original music for Piano solo.