Blue Grimoire

The Azure Grimoire in BlazBlue is the so-called "strongest" grimoire, also known as the "original codex" and can tap into the power of the Azure.

Information
Despite being called a grimoire, its form is not that of a book, but rather a high-density mass of concentrated seithr similar to the Black Beast. It has no fixed form and is currently imitating the right arm of Ragna the Bloodedge. Because it requires life force to function, Ragna absorbs life from other people. In actuality, Ragna's grimoire, along with Nu (v-13)'s is only an imitation. Terumi Yuuki was the one who created the Azure Grimoire. Terumi said that the Azure Grimoire's original form was a cauldron. The purpose of the Azure Grimoire is to gather souls. The Azure when released also has the ability to grant several advantages to its owner such as increasing their stats, producing a magical gylph to strain the enemy and doubles its user attack power as seen with the previous three users: Ragna, Terumi and Nu.

Mu is the one with the true Azure, inheriting it without the use of a Grimoire, though it takes Terumi tempering her in a new cauldron so it can be harnessed along with the power of the Eye.

Arakune is obsessed with finding the energy of the Azure. He hunts down those that exude the same energy or traces of the Grimoire. Coming into contact with the energy is what caused his form to degrade into the monster that he is. During his story, he manages to warn Litchi that she is being devoured by the energy as well, and that she should resist the temptation to embrace it any further.

Judging from what's been stated about smelting a Nox Nyctores, it takes thousands and thousands of souls. The reason the cauldron of Kagutsuchi is there is because it is where the 13th Prime Field Device, Nu was smelted. When the cauldrons are activated, a space time continuum is created to form a protective coccoon for the medium, and that's presumably the force for the Black Beast's time travel.

In one of Ragna's bad endings in Continuum Shift, after Rachel Alucard wins against Ragna in a fight, she tells him to "Never mistake the power of the Azure Grimoire as your own", Ragna responds by saying he will use his own power to shape his destiny. After Rachel leaves, Ragna's right arm begins to shake violently and seithr starts to generate. Ragna then sees an image of himself, being fully consumed by the darkness of the Grimoire. As quickly as this moment come does it vanish, leaving Ragna exhausted. Inside a Cathedral, Ragna encounters Jin Kisaragi, forcing him to use the Azure Grimoire. As Ragna wins, he loses the last of his self control and becomes the Black Beast itself, causing almost all of the planet to be destroyed. As Jubei and Rachel see Ragna off, she tells him that she is sorry, and that none of this was his fault and that she will see him in another world.

It is interesting to note that those who posess the Azure Grimoire be it real or an imitation are the "Blazblue" series boss characters two being male ( Ragna and Terumi) and two being female ( Nu-13 and Mu-12)

Owners of the Azure Grimoires
A list of those who have owned an Azure Grimoire (the real one and fakes)
 * Terumi Yuuki
 * Ragna the Bloodedge
 * Nu (v-13)
 * Mu (μ-12)

Activation
In each BlazBlue installment, the activation code seems to change throughout time for different characters:

"Restriction 666 released, Dimensional Interuption Imaginary Number Formed! Azure Grimoire, Activate!"

- Ragna

"Restriction 666 released, Dimensional Interference Field Deployed! Blazblue, Activate!"

- Ragna

"Restriction 666 released, Dimensional Interference Field Deployed! Now Engaging The Idea Engine! Blazblue, Activate!"

- Ragna, with the Idea Engine

"Restriction 666 released, Dimensional Interference Field Deployed! Code SOL, Blazblue, Activate!"

- Hazama