Caligula is based of the video game The Caligula Effect. μ, a virtual idol program that attained sentience and self-awareness, creates a virtual world, Mobius, for the benefit of humanity. People who are suffering in the real world or relate to μ's music, can be lured into Mobius.
The story follows Ritsu Shikishima, a studious high school student, that has just noticed that something is wrong. When he asks his friends about it, they just stare at him blankly. Upon graduation, Ritsu starts to realize, that his high school life, which μ considers "the most radiant time in a person's life", has been put on a loop. The end of the first episode is bizarre, but we will keep watching. You should too.