Prior to the events of BlazBlue, humanity was on the verge of extinction from a creature called the "Black Beast." The world was saved by six heroes who wielded magic. They helped humanity create "Ars Magus", a fusion of magic and science, to defeat the Black Beast. This event would be later known as the First War of Magic.
After the war, the Novus Orbis Librarium (the Library or NOL for short) was created to govern the world with the use of Ars Magus. A great deal of dissent was caused by the Library, partly due to Ars Magus' use in nearly every facet of society, and the widening socioeconomic gap between those who could and couldn't use Ars Magus. This dissent would eventually form years later into the Second War of Magic or also known as the Ikaruga Civil War, when the city of Ikaruga openly rebelled against the NOL. Upon winning the war, the NOL imposed a harsher rule on the world, punishing any rebellion against the NOL with death.
In December A.D. 2199, several years after the Second War of Magic, a branch of the NOL was utterly destroyed by an SS-class rebel named "Ragna" also known as the "Grim Reaper", in an attempt to destroy the Librarium. The NOL, hoping to stop him, immediately announced the largest bounty ever, available to anyone who could capture him. Interestingly, Ragna possesses a powerful form of Ars Magus known as the "Azure Grimoire." This led the NOL, as well as the other fighters, to hunt Ragna not just for his bounty, but also his Azure Grimoire.