Short answers, pulled from the story.
Fabula Nova Crystallis Final Fantasy is a subseries of games within the Final Fantasy franchise, all connected by a shared mythology focused on crystals tied to deities. Square Enix translates the Latin title as "The New Tale of the Crystal". It consists of seven released titles across multiple platforms, including Final Fantasy XIII and its sequels, Final Fantasy Type-0, and Final Fantasy XV.
Kazushige Nojima wrote the original Fabula Nova Crystallis mythology, starting in 2003 and finishing by February 2004. He drew on Greek and Norse mythology during his research. Creative input came from Yoshinori Kitase, Shinji Hashimoto, Tetsuya Nomura, Hajime Tabata, and Motomu Toriyama.
The series was originally announced at E3 2006 under the name Fabula Nova Crystallis Final Fantasy XIII. The three initial titles announced were Final Fantasy XIII, Versus XIII, and Agito XIII. The subseries title changed in 2011 when the "XIII" numeral was dropped.
Seven games have been released in the Fabula Nova Crystallis series as of 2016. They include Final Fantasy XIII and its two sequels, Final Fantasy Type-0, Final Fantasy Agito, Final Fantasy Awakening, and Final Fantasy XV.
Final Fantasy XV originated as Versus XIII, announced as part of the series in 2006. It was rebranded as Final Fantasy XV in 2011 and deliberately distanced from the Fabula Nova Crystallis brand for marketing purposes, with specific mythos terminology removed. The game retained thematic connections but reduced the mythos to a background element.
The three Final Fantasy XIII games collectively sold 11 million units worldwide. Final Fantasy XV sold five million copies on launch and had reached ten million units by May 2022. Type-0 sold over 740,000 units in Japan, and Type-0 HD shipped over one million copies worldwide by April 2015.