Allwise Infinite Maze is a secret/optional dungeon available after one beats the main part of the game.
It is found at the New Moon Inn, it is described by Allul as another option of Eesa's to the Hozone problem that had plagued the world, however eventually the Twelve Heroes of Noire decided on turning into Rogress. At the end of the dugeon lies a powerful Feldragon that is actually the transformed Thirteenth Hero of Noire. Allwise Infinite Maze was set up to be another dimension that houses the souls of those who inhabit it, thus if a person has died their soul can appear in the maze. However this place is incomplete and thus it is only a temporary reuinion with the person before they must depart again.
During the course of the dungeon L'Arc's group is assisted by the following departed characters as guest characters during certain floors.
The guest character will eventually leave the party when there section is through and of course they cannot be used out of Allwise Maze Infinity, however if the player returns to the section where the first met up with the guest they will proceed to join again for that section.
The very last section of this dungeon is done by the party without any guest assistance and culminates in the battle with the lost Thirteenth Hero of Noire.
The Maze possesses the strongest equipment available in the game, however they are ultimately inferior to the ultimate weapons one can have. It is strictly optional and is not needed to acquire said weapons.
The monsters start out in the lower 60's and eventually reach up into the lower 70's by the time the last floor is reached, with the Boss Allwise being the strongest foe in the dungeon. Also of note is that at the end of each section the player must get through a boss fight against a previously defeated boss (for example the first boss the player must fight is that flower boss that was fought in the Nabra Jungle. Beating the bosses at each section allows the player to continue through the dungeon into the next section and also allows the player to return back to New moon Inn via a teleporter.
The last point of interest is that there are no save points in Allwise Maze Infinity, so the player must return to New Moon Inn to save or to go visit another city for supplies. The player can return to either the beginning of the dungeon or to any of the ending parts of the sections of the dungeon, however as stated above the boss of that section must be dealt with first.