It's a visual novel by Type-Moon. The story revolves around a Lunar-princess hence the name Tsuki for 'moon' and Hime for princess. It is seen in the perspective of the protagonist Tohno Shiki who almost experience death when he was young and gained the Mystic Eyes of Death Perception that allows him to see death lines and sever them too, allowing him to kill anyone at will. I won't say any more to avoid spoiling the story.