Carn Dûm was the chief fortress of the realm of Angmar and the seat of its king. It was located at the northwestern end of the Mountains of Angmar, the north-western extension of the Misty Mountains.
Maps
Around T.A. 1300, Sauron's shadow became stronger and evil things multiplied, heralded by the reappearance of the Nazgûl. The lord of the Nazgûl came north and established the evil realm of Angmar between the Ettenmoors and the Mountains of Angmar on both sides of the Misty Mountains, because he intended to destroy the Dúnedain of the North and to exploit the disunity of the splinter realms of Arthedain, Cardolan and Rhudaur. He gathered many evil men, Orcs and other fell creatures in Angmar and became known as the Witch-king of Angmar. It is not known if Carn Dûm already existed when the Witch-king established the realm of Angmar or if it was built during his reign.
In T.A. 1409 a large army from Angmar invaded and devastated Cardolan, but a remnant of the Dúnedain of Cardolan defended the Barrow-downs or fled to the Old Forest. The last prince of Cardolan was slain in that year and was said to have been buried in the barrow in the Barrow-downs in which Meriadoc Brandybuck and Frodo Baggins were trapped by a Barrow-wight almost 1700 years later.
In T.A. 1975, the combined armies of Gondor, Lindon and Arnor crossed the river Lune and defeated the forces of Angmar in a great battle on the plain between Lake Evendim and the North Downs. The Witch-king of Angmar fled northwards towards Angmar with a remnant of his forces, but but his forces were overtaken by the cavalry of Gondor led by prince Eärnur and by forces led by the Elf-lord Glorfindel who came north from Rivendell before they could reach the shelter of Carn Dûm. The Witch-king was able to flee, but the remaining forces of Angmar were utterly defeated and no man or orc of the realm of Angmar remained west of the Mountains. As a consequence, it is possible that Carn Dûm was destroyed. It is also possible that Carn Dûm was repopulated after T.A. 2480, when Orcs began making secret strongholds in the Misty Mountains,.
On September 28 of T.A. 3018 while Meriadoc Brandybuck was trapped with Frodo Baggins by a Barrow-wight in a barrow in the Barrow-downs, he had a dream that he and others were attacked and defeated by the men of Carn Dûm at night and that his heart had been pierced with a spear. It is possible that he dreamt of the experiences of the last prince of Cardolan during the last hours of his life.