This is the traditional Scottish melody for Auld Lang Syne, a poem written by Robert Burns in 1788. Burns' poem and the melody it is commonly sung to are most likely based on existing Folk Songs handed down through oral traditions. Burns' version is now very well established in many parts of the world. It is often sung at special occasions, particularly New Year, Burns Night, and to mark the close of many events (including dances, cèilidhs, weddings and funerals) where the sentiment is one of celebrating goodwill and friendship, where all present will typically join hands in a ring. In Japan a song called "Hotaru no Hikari" is sung to the same melody, and it is played in shops and stores when they are closing.
The version presented here is arranged for Keyboard and we have another version arranged for Guitar. In addition we have the following PDFs with the sheet music for solo instrument: Main, High, Bass, Clar, Horn, Sax and Viola which can be used together with the guitar version or this Piano Accompaniment.
The image below is the first page of the sheet music, and here you can download the full sheet music for Auld Lang Syne for piano in PDF format.