Durin I (also known as Durin the Deathless) was the eldest and most renowned of the Seven Fathers of the Dwarves, and the ancestor of Durin’s Folk (the Longbeards), the most important family of Dwarves during the Third Age; he awoke in the Elder Days and came to Azanulbizar, east of the Misty Mountains. When he looked into the lake of Kheled-zâram (Mirrormere), he saw a crown of seven stars reflected above his head: he took this as a sign, and made his dwelling in the Misty Mountains, known as Khazâd-dûm (Moria).
Because of his long lifespan, he became known as Durin the Deathless; and his heirs were so much like him that they were named after him, as the Dwarves believed each one to be a reincarnation of Durin I.
Durin III was the King of Durin’s Folk during the Second Age at the height of the Dwarves’ friendship with the Elves of Eregion. He was given one of the Rings of Power – the Ring of Thrór – by Celebrimor.
Durin VI was King of Durin’s Folk at the time the Balrog was awoken in Moria. Durin VI was one of the first to be slain by the Balrog, which was thereafter known as Durin’s Bane.