The Infinite Dungeon is located in the south-east corner of the Drakalor Chain.
The ID is unique in that it is the only dungeon in ADOM that does not stay the same every time you visit. When you leave a level, it is destroyed and can never be found again. A new level will be randomly generated next time you enter. Most artifacts left on the ground in ID will return to the character's backpack when they leave the level; the Sceptre of Chaos is an exception to this. The ID is also unique in that most dungeon features such as pools, altars, and herbs will never be generated here. SIL can support some of these [altars at the very least]. Traps are still generated. Special rooms such as "smells like carrots" are also generated which can, in principle, be exploited to increase stats, particularly Appearance, Perception, and Learning.
The only guaranteed inhabitant of the ID is MaLaKaI the chaos knight, who can be found deep within the ID. There are, of course, many random monsters which, as usual for dungeons, will be more powerful on lower levels.
Despite its name, the Infinite Dungeon is not, technically, infinite. The lowest level that can be reached is limited by amount of memory allocated to storing the current level's number, which being a signed 32-bit integer, means that the deepest level of the ID is 2,147,483,647. After this, an integer overflow error will occur, which will propel the player back to I1. Practical considerations including the difficulty of the monsters, background corruption, and time required to reach this level, make this limit purely theoretical: assuming 10 seconds per level (which would be almost impossibly fast), over a thousand years of 24/7 playing would be required to reach the bottom.
If the player somehow manages to descend below I9999, the level counter in the status bar will instead say "I?".