The dungeon level is displayed to the far left of the status line. You start the game on dungeon level 1, where it might read:
Dlvl:1 $:1699 HP:13(13) Pw:5(5) AC:8 Xp:1/0 T:1
Dungeon levels and difficulty levels
Some game mechanics, such as the type and difficulty of monsters generated, are affected by the current level difficulty. Normally this is the same as the dungeon level, but in branches such as Sokoban that go upwards, level difficulty increases as depth decreases (the further you are into the branch).
However, if you are carrying the Amulet, the level difficulty is always the depth of the deepest level you have reached (i.e. the Sanctum). Furthermore, if you are in the Planes, this figure is increased by half your experience level (rounded down).
Mazes of Menace - outlining the list of levels in NetHack.