Once upon a time, there was an evil being called the Black Beast, a magical creature with multiple heads that terrorized the world. Conventional weapons and even nuclear bombs were powerless to stop it. Then one day, a small group calling themselves The Six Heroes [dun-d-d-DUNNNNNNN] stepped forth, invented magic and saved the day by slaughtering the Black Beast! YAY! Of course, when they finally took down the monster, it had already destroyed quite a bit of the world, and cutting off its various heads resulted in the beast spilling seithr around the parts that hadn't been spoiled. Think of seithr as a magical version of crude oil: it can be refined and harnessed for magical uses and even powers quite a few machines in BlazBlue's world of today. However, too much of it at once can apparently cause you to go insane and/or die.

Fast-forward several decades. After the Black Beast is dead, a group that would later be called The Library decides to govern what's left of civilization, and they heavily regulate how this seithr and the Ars Magus (the magical things you can do with seithr) can be used. Most people accept their rule, but at some point, one of the hierarchical cities named Ikaruga formed a union with those who did not like the way The Library is running things, and they sparked a civil war. Ikaruga fights valiantly, but the rebellion is instantly wiped out thanks to the Hero of Ikaruga, Major Jin Kisaragi, who bravely cut off the head of their leader! Though in reality, it was a (magical) sattelite laser cannon named Take-Mikazuchi that blew the crap out of Ikaruga. Also, Jin did end up freezing their leader Lord Tenjo in a block of ice. The survivors ended up fleeing to other cities, and the exist mostly as ronin now (including Bang).

A few years later, there's a rumor that a total badass called Ragna the Bloodedge, a.k.a. " Shinigami/the Grim Reaper" (depends on your language), is wiping out main branches of the Library in other cities one by one. And now Ragna has set his sights on Kagutsuchi, where the majority of CT (and CS, probably) takes place. The Library has posted a giant bounty on him that causes everyone to crawl out of the woodwork to hunt him down. Some want the massive reward, others want the Azure Grimoire that he is rumored to hold within his right hand, one of the most powerful Armagus out there, if not THE most powerful.

There's a lot more shit that I don't feel like getting into here, though you can read each character's wiki page here (disclaimer: I've done some work on them) for their individual stories or I might talk about them later if I'm feeling particularly bored. Basically, everyone's story is technically true except for the fact that there's one common factor to all of them: in the end, v-13 stabs Ragna and drags him with her into a magical Cauldron buried deep within the Library, forming the Black Beast which then somehow gets transported back into the past thanks to the aforementioned satellite laser cannon that hits the Cauldron at the same time, thus erasing the events from history over and over and over...until the True Ending pops up.

In the True Ending, Noel saves Ragna from falling into the Cauldron with v-13, Ragna discovers that she is a clone/image/whatever of his supposedly dead sister Saya, and Rachel pops up to say that Noel actually has the real Azure Grimoire while he and v-13 only have fragments of it. Then she activates the Tsukiyomi Unit, a giant magical shield that blocks the satellite laser from destroying everything again. However, it turns out that this was planned by the evil Terumi, who kept manipulating events and continuing the time loop until he could acquire the True Azure Grimoire through Noel's gaze (don't ask me how, he just did). Once he gets it, he beats up Ragna a little, then escapes to continue the next part of his evil plan. In the epilogue, he uses his identity as Hazama to conscript Tsubaki, another graduate of The Library's military academy, to hunt down Jin and Noel for treason against The Library, forcing Tsubaki to juggle her friendship to them and her duty to her superiors.