In the Magister's City: Ishana, there is an ancient legend, saying that the Grimoire possesses the power of the God of Calamity, and that the one with permission, will be shown the Logic of the world, the Azure. The Grimoire has the power to connect to the Boundary and draw out the power of the Black Beast residing within it, much like the Azure Grimoire.
It has two abilities, the first of which is the Awakening Release (XBlaze), which uses positive feedback to store seithr into power to be used at a later date. The second known ability is the Restriction Release (Soul Eater) which creates a black mist that drains all it touches.
Physically, the Grimoire is a crystal made out of super compressed seithr, and is actually a part of the Black Beast; however, Tōya was long unaware of it being a part of him.
"Me" has a copy of this Grimoire, however, it has no connection to the Black Beast, and just works as a limiter for her ability to attract seithr.