Izayoi

Izayoi (十六夜,いざよい) is the mother of the title character Inuyasha.

History
Izayoi was the daughter of a feudal lord, and at one point was held captive by the samurai Takemaru no Setsuna. Takemaru planned to use her to lure Inu no Taishou into a trap to kill the Daiyōkai. Though Izayoi told Takemaru to leave in order to spare him from the Inu Daiyōkai's wrath, Takemaru said that he still loved her, and killed her, but not before she gave birth to Inuyasha. The Inu no Taishou overpowered Takemaru's men only to discover his beloved dead, but then he used Tenseiga to revive her. Inu no Taishou gives Izayoi the Robe of the Fire Rat and then orders to escape with their son, whom he names "Inuyasha". She follows her beloved's instructions and leaves. Unfortunately, her lover was already injured badly in an earlier battle with the dragon yōkai, Ryukotsusei. The injuries weakened the Inu no Taishou enough so that when the mansion collapses on both him and Takemaru, he dies along with Takemaru. This sets up Izayoi to raise Inuyasha on her own.

Very little is known about Izayoi as she died before the events of the series takes place and because Inuyasha rarely speaks about her, most likely because he is still saddened by her death. At some point she met and fell in love with Inu no Taishou, who returned her affection. Although the two form a relationship it is never specifically stated if the two were married or officially mated. When Inu no Taishou died she was forced to raise their Hanyō son Inuyasha alone, with the regret that her son would be discriminated by both humans and yōkais alike for his hanyō heritage. She died when Inuyasha was a young child.

Izayoi's name is never given in the manga or the anime series. She is given the name Izayoi in the third movie. Sesshomaru, Inuyasha's elder half-brother, uses a yokai to make a perfect duplicate of Izayoi in order to trick Inuyasha into revealing the whereabouts of their father's demon sword, the Tessaiga. Sesshomaru blames Izayoi for his father's death, claiming that she had made the Inu no Taishou weak which lead to his death. The manga never elaborates on Sesshomaru's claim, however the third Inuyasha movie attempts to fill the gap. The Inu no Taishou went to rescue Izayoi right after his battle with Ryukotsusei, despite having life-threatening injuries. The wounds ultimately weakened him enough to where he is killed by a collapsing palace, something he most likely would have survived had he not been injured. Since the events of the third film are never mentioned in the manga, they are not considered canon. Sesshomaru could have also meant that had the Inu no Taishou never loved Izayoi, he would have been strong enough to kill Ryukotsusei. Like her daughter in law Kagome Higurashi who was protected by her son, Izayoi was protected by InuTaisho's sword.

Inu no Taishou
Its very little well known how or when Izayoi met the dog general, If they were married or how they ended up having a child. However its clear they both cared and love each other deeply. Seeings how after his battle with Ryukotsusei insted of tending to his wounds he rushes to his new born son which he names Inuyasha. Finding Izayoi dead he uses Tenseiga to revive her. He's often called "My Dearest" by Izayoi. Before he died he told her "Izayoi you must live a long life, Live long and well with Inuyasha." It clearly shows he love her.

Inuyasha
Was the half demon son by Izayoi and Inu no Taishou. Inuyasha had a special relationship with his mother seeing how she was the only parent to raise him until her death. Whenever someone talks bad about her Inuyasha gets very defensive. He prefers not to talk about her which shows he misses her lot. Time by time he often vists his mother grave planting new flowers. Just like his father, Inuyasha cares for humans. Izayoi often cried to her son knowing what his life would be like not being accepted by humans or demons. She loved and cared for her son wholeheartedly.

Trivia

 * Izayoi is the name given to the night of the 16th of every month. The Japanese believe that on that date, the night is more beautiful.