Arnor:

The North Kingdom of the Dúnedain, Arnor was founded in the year 3320 of the Second Age, after the Downfall of Númenor. Its founder was Elendil, who was the High King of both Arnor and Gondor (founded by his two sons, Isildur and Anárion). The tenth King of Arnor, Eärendur, split the realm between his three sons, so it was later called Arthedain, Cardolan, and Rhudaur. In Cardolan and Rhudaur, the Dúnedain soon dwindled enough that by 1350 of the Third Age, it was overtly allied with Angmar, the realm of the Witch-King. After the destruction of Angmar, the line of Arnor's Kings never failed, though Arnor was ruined, and the Kings were called Chieftains instead. It was from this line that the Kings of Gondor eventually came from too, with the end of the Third Age and Aragorn's crowning.

Arthedain:

When Eärendur, the last king of Arnor died in the year 861 of the Third Age, the country was split into three separate kingdoms: Arthedain, Cardolan and Rhudar. Arthedain, which contained the former capital city of Annúminas was given into the rule of Amlaith, the eldest of Eärendur's three sons. It was through this kingdom that the line of Isildur was maintained, as the line of Arthedain's kings outlasted those of Rhudar and Cardolan.

The borders of Arthedain extended from the Lhun and the Brandywine, and as far east as Weathertop and contained the two palantiri belonging to the Men of the North. One of the Palantiri was located at Amon Sûl. The capital city of Arthedain was at Fornost.

In the year 1349 of the Third Age, after the end of the royal lines in Rhudar and Cardolan, Argleb I claimed kingship over all of the lands that originally made up the realm of Arnor. However, that claim was contested, leading to war, which led to the end of all three regions as formal kingdoms. After this, the royal family of Arthedain continued in secret as the Chieftains of the Rangers of the North.

Annúminas:

The first capital of Arnor, Annúminas, was deserted when the capital city removed to Fornost. Annúminas was rebuilt during the reign of King Elessar during the Fourth Age.

Angmar:

The realm of the Witch-king, later discovered to be the chief of the Nazgûl. It lasted for approximately 700 years. Angmar was the enemy of the northern kingdom of Arnor.

Angband:

Melkor's stronghold, built after he destroyed the two lamps it was built under the Ered Engryn. Though it was partially destroyed when the Valar captured Melkor, it was not completely cleaned out and Balrogs and others still hid there during his captivity. After he escaped from Valinor, Melkor rebuilt it and it was never again taken until the Great Battle that ended the First Age of the Sun. Angband was, of course, destroyed when the most part of Beleriand sank beneath the ocean.

Aman:

The Blessed Realm, and the home of the Valar after Melkor destroyed Almaren. When Eru changed the shape of the World during the Downfall of Númenor, Aman was removed from the circles of the World, in such a way that only the ships of the Elves, could return by the Straight Road. Aman had many names of which the most common were, The Blessed Realm and the Undying Lands.

Arda:

Our World.
Before the downfall of Númenor, Arda was flat, encircled by a great sea. However when Eru changed the shape of the World and destroyed Númenor, the world was made round, like it is today.

Archet:

A village in the Bree-land where Hobbits and Men live together. Archet is located to the north of the Chetwood.

Amon Anwar (The Hill of Awe):

The hill within the Firien Wood, later used as a beacon in , the line of beacons between Gondor and Rohan. Prior to the coming of Cirion, Amon Anwar was the site of the tomb of Elendil. Isildur set it there as being the center of the Realm of Gondor as it was at that time. Being a holy place it was chosen for the oath of Cirion and Eorl. After that time, Elendil's tomb was removed to the Hallows in Minas Anor, seeing as the hill was no longer the center of the realm, but on it's border. After that the hill became one of a line of beacons, and being on the border, its upkeep was by both men of Gondor and of Rohan, though later the upkeep fell

The Anduin River:

Also called the Great River, clearly this is one of the largest, if not the largest, river in the north-western part of Middle-Earth in the Third Age. It started in the Grey Mountains and roughly paralleled the Misty Mountains on the eastern side. At one point in history, hobbits lived on the banks of the river, though they later migrated North and West.

Only three permanent crossings are described. The first is the Carrock, near the High Pass. It is a ford with a rock in the middle. The second is called the Old Ford, fairly close to the Carrock. The third was destroyed by the time of the War of the Ring. It was the bridge in Osgiliath. The only other method of crossing was by swiming (as attempted by Isildur) or by boat.

The river passed by or through the realms of Gondor, Rohan, Lothlórien and the region of Rhovanion. Landmarks along it's course included the Gates of Argonath, Tol Brandir, and Rauros.

For many years, from the Battle of the Gladden Fields, when Isildur was slain, the River hid the One Ring. It was several centuries later that the Ring was found by two hobbits, Déagol and Sméagol.

During the War of the Ring, when the Company was passing down the River, the Eastern side of the lower Anduin was dangerous because it was patrolled by Orcs. The western bank however, was still believed to be safe, although this was disproved when the Company was attacked at Parth Galen.

The Argonath:

Also called the Gates of Argonath and the Pillars of the Kings. Early in the Third Age, the cliffs on each side of the Anduin River at a narrow point were carved into giant figures of Isildur and Anárion. Each of the figures had it's left hand raised in a warning gesture. In the right hands was an axe, and on the heads was a combination of helm and crown.

Beyond the figures, the river widens again. This was where the lawn of Parth Galen and the hills of Amon Hen and Amon Lhaw were to be found.

Amon Sul:

The southernmost hill in the chain of the Weather Hills. The Road skirts along the edge of the hill. In the time of Elendil, there was a tower on the hill. The ruins were still there at the end of the Third Age of the Sun, when Frodo and the others were atacked by the Nazgûl. By that time, the place was known as Weathertop. The location was perfect as a look-out point, as from the top of the hill a person could see for leagues around.

The Hobbit
The Lord of the Rings
The Silmarillion
The Complete Guide to Middle-Earth by Robert Foster
The Unfinished Tales