From the pen and mind of JRR Tolkien, Thrain I was the first King under the Mountain until his death in 2790. Thror became King under the Montain centuries later. Thrain I was born in 2542 and was murdered in 2790 at Moria, where he lost one of the Rings made for the Dwarves. His son Thrain II was sent wandering with the lust for the Ring in 2841, and in 2850 he was killed at Dol Guldur, where the Ring he had found in his wanderings was taken from him by Sauron.
Thorin Oakenshield II, who was a Dwarf of great importance (since he was a descendent of Durin) set off in The Hobbit with the information from his father, Thrain II, which included a map and key to the Lonely Mountain. He was finally killed during the Battle of the Five Armies at the end of The Hobbit, along with Fili and Kili, who were the sons of his sister Dis.