Rinnegan

The is reputed as the most exalted eye amongst the "Three Great  Dōjutsu  ", the others being the Sharingan and the Byakugan. It is said that in times of disorder, one who wields the Rinnegan is sent down from the heavens to become either a "God of Creation" who will calm the world or a "God of Destruction" who will reduce everything to nothingness. The Rinnegan is characterised by a ripple pattern that spreads over the eyeball.

Acquisition
The Rinnegan was first manifested by Hagoromo Ōtsutsuki in the Shinobi World, derived from the Rinne Sharingan wielded by his mother. It is suggested his Rinnegan was a kekkei mōra, and with it, he saved the world from the Ten-Tails and created ninshū, the precursor to modern ninjutsu. In the anime, after experiencing the trauma of loss, Hagoromo awakened his Mangekyō Sharingan which almost instantaneously progressed to become Rinnegan. For his contributions to the world, Hagoromo became revered as the Sage of Six Paths, and both he and his eyes rose to mythological status over the centuries that followed; even when the Rinnegan was later proven to exist, it was regarded by some as merely a mutation.

The Rinnegan can typically be awakened by gaining Hagoromo's chakra either by reproducing it from combining the chakra of Hagoromo's sons, Indra and Asura, or by directly receiving chakra from Hagoromo himself. Black Zetsu spent centuries attempting to manipulate the reincarnations of Indra and Asura into awakening the Rinnegan. It was not until the time of Madara Uchiha - Indra's reincarnation - that this was successful, when Madara infused himself with the DNA of Hashirama Senju - Asura's reincarnation. However, Madara's Sharingan did not become Rinnegan until decades later, at nearly the end of his natural lifespan; this also restored the eyesight lost from his use of Izanagi. When Kabuto Yakushi reincarnated Madara, he operated under a similar hypothesis that Sharingan can be evolved into Rinnegan through combination with Hashirama's DNA. To that end he successfully recreated the Rinnegan in Madara's reincarnated body, though these fake eyes did not have full access to the original's abilities.

After receiving half of Hagoromo Ōtsutsuki's chakra, Sasuke's left Eternal Mangekyō Sharingan made way for the Rinnegan and remained visible as six tomoe, three on each of the two innermost circles of the eye. Should Sasuke's chakra reserves fall to a certain level, the tomoe vanish along with the Eternal Mangekyō Sharingan in his right eye and he is unable to use its techniques.

Contrary to Madara and Sasuke's cases in needing Hagoromo's chakra, Momoshiki Ōtsutsuki has Rinnegan in the palms of his hands. Initially, his Rinnegan are red, but they become purple (in the movie), or yellow (in the manga) after he absorbs Kinshiki. This also grants him a third Rinnegan on his forehead.

As with any dōjutsu, the Rinnegan can be transplanted into others. Prior to his death, Madara implanted both of his eyes into the young Nagato without the boy's knowledge, and he was able to make effective use of the Rinnegan throughout his life due to his Senju lineage. After Nagato's death, the Rinnegan were taken by Obito Uchiha, who implanted the left eye into himself and hid the other because he could not handle the power of both eyes at once. Madara later reclaimed both of his Rinnegan after he was revived and ultimately died with them.

Abilities
The Rinnegan grants the wielder a wide range of abilities without any known chakra requirement to keep the eyes active. Certain abilities are only available to the original owner of the dōjutsu, but possession of even a single transplanted Rinnegan can grant overwhelming power. Rinnegan are able to see chakra, as well as its flow within the body and the activated tenketsu of the Eight Gates, but cannot see through obstructions such as smoke bombs. One who possesses the Rinnegan can easily master any jutsu as well as all five nature transformations, create black receivers into which they can transmit their chakra, fully decipher the stone tablet written by Hagoromo, and counter the effects of the Infinite Tsukuyomi.

Possessing the Rinnegan grants the user a family of abilities collectively known as the Six Paths Technique: control over attractive and repulsive forces with the Deva Path; the ability to mechanise one's body with the Asura Path; soul extraction through the Human Path; the menagerie of summons available to the Animal Path; chakra absorption through the Preta Path; and access to the King of Hell through the Naraka Path. These abilities can be distributed to the Six Paths of Pain — six bodies embedded with black receivers, which the user can control remotely. A seventh ability, the Outer Path, is said to allow the user to preside over life and death, granting the ability to revive the dead. The user is also able to summon and control the Demonic Statue of the Outer Path, as well as manifest chakra chains to bind the tailed beasts. The dōjutsu also grants the user a shared field of vision with the Six Paths of Pain, the King of Hell, and the Animal Path's summons, all of which possess copies of the Rinnegan.

Certain Rinnegan abilities have only been demonstrated by single users: Madara can create corporeal shadows in the invisible world of Limbo, which is only visible to the Rinnegan; Sasuke's Rinnegan allows him to shift spaces within a certain range of himself, and create portals to other dimensions; Momoshiki is able to absorb any ninjutsu with his right Rinnegan and subsequently release it from his left, and also with the form transform others into chakra-filled edibles.

Sasuke’s Rinnegan had several sciences to it, and one of them was pattern recognition. It helped him analyse patterns inside codes, and by comparing them to similar patterns, decipher what was written. When put into use, one could take large amounts of information from a small amount of text.

Trivia

 * is the Japanese term for Samsara, the cycle of reincarnation or rebirth in several Indian religions. This is reflected in the names of the Six Paths Techniques, which share their names with the six Samsaric realms of reincarnation.
 * The kanji is also used in Sharingan and Rinne Sharingan, potentially linking the three terms etymologically.
 * When it first appeared in the anime, the Rinnegan was depicted as multicoloured. This was corrected after the Rinnegan was depicted in colour in the manga. However, whereas the Rinnegan in the manga is a uniform shade of purple, the anime tends to make the centre-most ring a slightly darker shade of purple.
 * In the manga, when Deidara and Sasori brought Gaara to the Akatsuki hideout, Pain was depicted with tomoe in his Rinnegan in one panel. This was corrected in the tankōbon release of volume 29.
 * In episode 203, digital coloured editions of chapters 676 and 678, and in the sixteenth opening of Naruto: Shippūden, the Rinnegan are depicted red.
 * Though usually depicted with six, the manga has portrayed Sasuke's Rinnegan with varying numbers of tomoe on various occasions:
 * In its manga début, it appears to contain nine tomoe.
 * Twice while visualising Limbo, it contained no tomoe.
 * While shielding Team 7 from the Infinite Tsukuyomi, it contained no tomoe.
 * While sealing Kaguya Ōtsutsuki, it contained no tomoe. This was corrected in the tankōbon release of volume 71.
 * On the back cover of Jin no Sho, it contains three tomoe.
 * In the anime, within the Jiraiya Ninja Scrolls novel, the Rinnegan has the ability to see through solid objects.
 * In Naruto Shippūden: Ultimate Ninja Storm 4, Sasuke's Rinnegan is erroneously referred to as a Rinne Sharingan.