Blue Grimoire

The Azure Grimoire (蒼の魔道書), also known as the BlazBlue (ブレイブルー) 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. It originally had the form of a jet black rock shaped in the fashion of a human without a head when it was in the possession of Rachel Alucard. After Ragna the Bloodedge touched it, it crumbled, turned into a mist, swallowed him in darkness, and then took the form of his right arm, despite still having the same obsidian blackness. Because it requires life force to function, Ragna absorbs life from other people. In actuality, Ragna's grimoire, along with Nu-13's grimoire, is only a prototype. Hazama is the original creator of the Azure Grimoire. Terumi said that the Azure Grimoire's original form was a Cauldron, whose purpose 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 glyph to strain the enemy and doubles its user attack power as seen with the previous three users: Ragna, Hazama and Nu.

Mu-12 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 cocoon for the medium, and that's presumably the force for the Black Beast's time travel.

In Ragna's Bad Ending in Continuum Shift, after Rachel 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.

Owners of the Azure Grimoires
A list of those who have owned an Azure Grimoire
 * Hazama
 * Ragna the Bloodedge
 * Nu-13

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

Trivia

 * "Code" is another word for Grimoire. "S.O.L." is short for "Souls of Language".
 * Hazama's addition to the activation chant, "Code S.O.L.", could be either a reference to Sol Badguy, the protagonist of the Guilty Gear series of games, or (less likely) a sly joke relating to the phrase "S*** out of luck", which is often abbreviated as "SOL".