Arthedain (Sindarin for "Realm of the Men") is the name of one of the three kingdoms into which Arnor was divided in III 861 (the other two being Cardolan and Rhudaur). Arthedain included what is now the Shire, as well as most of Bree-land and North Downs. The Weather Hills, including the tower of Amon Sûl, belonged to Arthedain but were contested by Cardolan and Rhudaur. Arthedain was the westernmost division of what had once been Arnor.
Amlaith, the first King of Arthedain, moved the capital to Fornost. The kingdom and its capital flourished for roughly a thousand years, until it was destroyed by an invasion from Angmar in III 1974 - 1975, which ended with the Battle of Fornost. After this point, the surviving Dúnedain of Arthedain scattered and began to call themselves the Rangers of the North, having no kingdom anymore but gathering under chieftains, eventually leading to Aragorn.