The story in Notes takes place on Earth in the distant future. After mankind killed the planet on which it lived with pollution and warfare, all natural life died with it. Only ones surviving were the humans, as they were able to use technology to artificially sustain themselves. They eventually created enhanced humans, which were able to live on the ruined planet, and A-rays, creatures created with genetic engineering by combining humans and various other extinct life forms.

A war breaks out between enhanced humans and A-rays, resulting in complete devastation of what was left of Earth, as well as the near extinction of enhanced humans. The war was interrupted by the arrival of 8 Aristoteles, who only seek to indiscriminately destroy all remaining life on the dead planet.

Note: Commonly referred to as Angel Notes.

(Source: Type-Moon Wikia)