Izanagi (伊邪那岐, 伊弉諾) is a Japanese creation deity born of the seven divine generations in Japanese mythology. He is also referred to in various chronicles such as the Kojiki and Nihon Shiki as Izanagi-no-Mikoto (伊邪那岐命, 伊弉諾尊), the "male-who-invites."
In marriage, he and Izanami have created many of the islands (all sans Onogoro Island) and deities of Japan. When Izanami died, Izanagi tried to retrieve her from the underworld, but failed. He mistakenly looks at her while she's in a rotting, monstrous state in the underworld, which shames her. She attempts to kill him, and swears to kill a thousand of his men a day. Izanagi retorts that he will make sure that a thousand and five hundred will be born each day.
After returning to Earth, Izanagi performed a cleansing ritual in the river Woto. During that, from his left eye is born Amaterasu, from his right eye, Tsukiyomi, and from his nose, Susano-o. Izanagi separates the visible world among the three, with Amaterasu getting control over the cultivation and crops, Tsukiyomi over the moon and night, and Susano-o over the sea, the storms and the winds. After this story, Izanagi no longer appears in myths.
The protagonist, Akemi Nakajima, is the reincarnation of Izanagi. After being tricked into summoning Loki, he begins to experience visions of his previous life as Izanagi. He later teams up with Yumiko Shirasagi, who is the reincarnation of Izanami, to defeat Loki.
Megami Tensei II
Izanagi first appears in Asmodeus' Cave after the hero defeats the demon lord. Later, after Izanami is revived and the Palace Ring is obtained, Izanagi will teleport him from Frontier Island to Lucifer's Temple.
Shin Megami Tensei III: Nocturne
If the Demi-fiend manages to achieve a qualifying Press Turn count on all the Burial Chambers in the Labyrinth of Amala, then he will be awarded an extra Turn Press by Izanagi and Izanami during a second playthrough. This is accomplished by meeting with Cerberus in the first Burial Chamber of the First Kalpa and following him to the secret Tomb of Yomi in the 666th basement of the Labyrinth.
They will mention how they had waited for a strong person such as the Demi-fiend to appear so that they could entrust them with their power. Before leaving, they ask him to pursue the path of creation and mention how their powers were lost due to the destruction of the old world. They mention that both Izanami and himself were the creators of the old world.
"One of the ancient gods who existed before Japan was formed. He created the Ouyashima from chaos, then gave birth to countless children and laid the foundation of soil and nature."
—Persona 4 compendium
In Persona 4, Izanagi is the protagonist's Initial Persona. When the protagonist first encounters the Shadows, Izanagi's voice prompts him to awaken to the power within. The protagonist then mutters the word "Persona" and summons forth Izanagi.
In the events of the Normal Ending, Tohru Adachi is capable of invoking a bloodied, more malevolent form of Izanagi, called Magatsu-Izanagi. While the Investigation Team is surprised at the similarity of Adachi's Persona to that of the protagonist, the events of the True Ending reveals that the protagonist, Adachi and Namatame actually "received" their Personas from the Moel Gas Station Attendant, whose true identity is revealed to be Izanami. According to Izanami herself, she gave the Persona of Izanagi to three outsiders who represent Hope, Despair, and Emptiness.
The protagonist represented Hope and thus his Izanagi is "pure." Adachi represented Emptiness, and as he refused to see the truth and gave into murderous corruption his version of Izanagi became tainted and malevolent as well. Namatame, presumably, would also receive another version of Izanagi, which represented Despair, reflecting his desperate idea of "saving" people from the murders by throwing them in the Midnight Channel, although his Izanagi is never shown in the game.
During the True Ending's final sequences, in the protagonist's final confrontation with Izanami-no-Okami, he gathers the strength of the heart accumulated by his Social Links and forms The World Arcana, transforming Izanagi into his true, standalone form and most likely the protagonist's true Persona — Izanagi-no-Okami. The Persona easily dispatched Izanami-no-Okami with his Myriad Truths skill.
However, like Aigis and Athena, Yu is limited to Izanagi and cannot change Personas during fights, save for his Instant Kill.
Also unique to this game is that Izanagi knows the skills/spells Swift Strike, Ziodyne and Cross Slash; the former two while not possible for the default Izanagi Yu starts with, it is possible to recreate another Izanagi with those two skills in the original Persona 4 and in Golden.
Izanagi can use a bass guitar as his instrument after completing a song.
"A Persona of another story. One of the ancient gods who existed before Japan was formed. He created the Oyashima from chaos, then gave birth to countless children and laid the foundation of soil and nature."
—Persona 5 compendium
Izanagi appears as a DLC Persona, alongside an alternate version of him called Izanagi Picaro. Izanagi, along with Orpheus, are paid $2.99, though he can be downloaded for free if the player ordered a digital pre-order copy of the game.
Devil Children Black Book/Red Book (PS)
Izanagi is a level 99 Battle Net opponent in Red Book. He uses his children Tsukuyomi, Susano-o, and Amaterasu as his personal demons. He awards Mirai Kaname with Amaterasu after being defeated.
Lord of Vermilion Re: 2
Izanagi appears alongside Pallas Athena, Thanatos and Messiah as one of the Personas featured in Lord of Vermillion Re: 2, once again serving as Yu's Persona, using Ziodyne as his skill.