Persona is technically a spin-off series, the main series is Megami Tensei (often called megaten for short) and is sort of a shared universe for a lot of games.

Shin Megami Tensei, Devil Survivor, Devil Summoner, Catherine (sort of), Tokyo Mirage Session (very loosely connected) are some of them.

They're all urban fantasy, mostly set in Tokyo. Protagonists are almost always a group of Tokyo students caught in a sudden demon invasion. Demon in this context is actually any kind of supernatural beings people can believe in, including actual demons from hell, gods from all mythologies, folklore creatures, angels, urban legends, ghosts, legendary beasts and heroes, whatever.

Another main concept of that series is the Demon Summoning Program, a way for humans to contract and summon demons to their side using a computer or a handheld device of sorts. So there is generally a creature collecting element to those, like a dark and violent Pokémon that actually predates Pokémon. Rather original, lots of these games let you negotiate with enemy encounters to try to recruit them.