The Capitol Building

Before the Great War, the United States Capitol Building housed the legislative branch of the government of the United States. It is located in Washington, D.C., on top of Capitol Hill at the east end of the Capital Mall. The other side of the Capitol opens onto Seward Square.

Sections
The building is broken into a number of areas. The most common way to enter the building is from the west side of the building from the mall, and this takes you to the appropriately-named "Capitol Building West Entrance". One can also explore the "Capitol Building East Entrance", the "Conference Room", and the "Hall of Columns". The Rotunda, although centrally located, is considered part of the "Capitol Building West Entrance".

The Battle for the Capitol Building
The Capitol serves as the battleground for a major conflict between the Super mutants, Talon Company and the Enclave , although its not unheard of for there to be slavers, raiders, or Brotherhood of Steel Knights there as well.

An Enclave Vertibird and kill team (with an Enclave-controlled Deathclaw) may be encountered on the steps of the Mall side of the building, while the rotunda of the building hosts a Super Mutant Behemoth (see Super Mutant Behemoth below). Not only are there super mutants near the rotunda of the building, there are also super mutants right before you go up the steps to the building.

Super Mutant Behemoth
The Super Mutant Behemoth can be found in the Capitol Rotunda. There are two ways to go about killing him.

If you just want him dead, the smartest move would be to enter the hallway next to the entrance to the dome area, this should lead you to a terminal you can hack to activate the turret system. Remember to deactivate the turrets, as they will be hostile to everything in the room. After he is taken down, you can loot the various mercs and mutants for a large amount of ammo. There is also a large cache of missiles you can access once the room is clear - a missile launcher is provided as well, you don't even have to bring one. Even without hacking the turret, if the player stays completely out of the battle, the Talon Company Mercs may defeat the behemoth on their own, due to superior numbers and the fact that one of them may carry a Fat Man. It is important to note that the merc with the Fat Man is a hostile NPC. If you don't want you or your companion getting killed rush into the dome, target him in VATS, steal the weapon and run for it. If the merc drops the Fat Man, be sure to beat your companion to the weapon. Companions do not take the blast radius of the Fat Man into account, often with disastrous results.

If you wish to take him down yourself for experience, be wary of the mercs. As stated before, one comes equipped with a Fat Man, so it would be wise to enter sneaking mode and quickly take him out. At that point, he should go down with one or two Mini Nukes or a few missiles. There is also a super mutant with a Minigun on a ledge in the back of the room (the corpse will fall down, the ground isn't even, so it slips down). If you are low on ammo, there is a surprising amount on the corpse of the behemoth.

One should be wary of idiotic actions that companions might take. The hallway facing the rotunda is completely safe from the behemoth, but, in spite of the ability to attack the enemy without reprisal, companions have a propensity for running in close to attack. If you are traveling with companions you may want to tell them to wait out of line-of-sight of the rotunda so that they can't see the behemoth or any other enemies within and will not rush to the assault. The Talon Company Mercs will take out most of the super mutants within leaving only behemoth. Once it is down to just the two of you, you can happily VATS him with the Plasma Rifle or anything else without injury.

It's a miracle how they got the behemoth in there in the first place, since he doesn't fit in the hallways at all. It's possible he entered through the big opening in the roof dome. Though, considering that the Capitol has been a stronghold of the super mutants for some 100 years, it's also possible that he was the oldest one, and eventually grew into a behemoth, inside of the Capitol.

Note that due to an occasional bug, the behemoth can sometimes actually move out of the rotunda and into the room immediately proceeding the said rotunda. In this case, retreat into the corridor to avoid being attacked.

Capitol Building West Entrance

 * Nikola Tesla and You on a desk behind a [hard] locked door.
 * U.S. Army: 30 Handy Flamethrower Recipes on a table, southeast part of the Capitol dome
 * Mini Nukes and a Fat Man on opponents and/or on shelves inside the dome

Capitol Building East Entrance

 * Tales of a Junktown Jerky Vendor on the middle desk in a row of three cubicles
 * Pre-War Book on a fallen cabinet next to that desk
 * Nuka-Cola Quantum a room over to the east, behind a coffee maker

Conference Hall

 * Lying, Congressional Style appropriately stashed on a podium.

Hall of Columns

 * D.C. Journal of Internal Medicine on the upper level. A Talon Company sniper is stationed on a bridge, and the book is on a railing facing south. If it is not there it was knocked down in the fire fight (this is common) just reload or look for it on the floor below.
 * Chinese Army: Special Ops Training Manual behind a {hard} locked door (accessed from a small hallway found near a turret and a locked turret control terminal in the middle of the hall)

Gallery and concept art
On May 8, 2007, Bethesda Softworks released a piece of Fallout 3 concept art by Craig Mullins depicting the Capitol after the Great War. This picture appeared then in an apparent terrorist threat, said to be shown in some islamist forum as a real-life would-be scenario, according to media. Source: http://www.news.com.au/al-qaeda-urges-use-of-wmd/story-e6frfkp9-1111116473744