Rido Kuran is Yuki's estranged uncle who intended to sacrifice Yuki as a child. Later on in the series, instead of drinking her blood as food, Rido decided to try and take Yuki as a 'lover' replacement for Juri, her mother whom he loved.
As a child, Yuki had nightmares of a pair of Heterochromic eyes (one blue, one crimson) staring at her for long periods of time but she thought nothing of them as she had Kaname Kuran to protect her. The eyes were later revealed to belong to Rido Kuran; the uncle of Yuki who is in love with Yuki's mother, Juri. However, this love was unrequited and Juri had fallen in love with her other brother Haruka. Once Rido discovered the existence of Yuki, he planned to abduct and sacrifice Yuki, similar to what he had done to her real brother, Kaname. However, his intentions behind it are unknown. His attempt was stopped by Haruka and Juri at the cost of their lives and Yuki's vampire-self was sealed away in hope of her leading a normal and safe human life with her adoptive father, Kaien Cross, while Rido was forced to go into a deep slumber, after his body was mutilated horribly by Kaname the Ancestor, who has taken the place of Yuki's real brother.
Rido first appeared in the possession of a little vampire boy whom Yuki spotted crying in the streets one day because he lost his mother. After Yuki led him to the place supposedly of where his mother was, the little boy thanked her with a kiss on the cheek. This sucked some vitality from Yuki, causing her to faint, but at the same time, Rido managed to put some of her forgotten vampire memories into her head. Whilst Yuki had become distressed about not knowing her past and then haunted by the few brief ones that had surfaced, Rido had re-awakened with the help of his son Senri Shiki and had possessed his body. Rido, in Senri's body, had entered Cross Academy in search of Yuki and thus putting Yuki in danger once again. His appearance forced Kaname to reawaken Yuki as a vampire again. Later on, after Yuki manages to wield Artemis again, she encounters Rido and he notices the likeliness between Juri and Yuki then changes his intention of killing her, to replacing Juri. Because of this, Rido continuously talks to Yuki as if she were Juri; asking her why he wasn't good enough, what he was missing etc. possibly as a way of him trying to get his feelings across to Juri. As Rido proves to be far too strong for Yuki to handle, she and Zero temporarily form an alliance in order to defeat Rido. Yuki eventually impales Rido in his heart as he embraces her from behind and then, Zero finishes him off with his Bloody Rose as Rido caresses her cheek with his last ounce of strength.
Rido's obsession with Yuki had most likely stemmed from his unrequited and deep love for Juri, her mother. He had tried many times to make her fall in love with him, only for her to fall in love with his younger brother, Haruka. That would have had a negative effect on his already unstable mind. His abduction and murder of Kaname could have been a way of him getting revenge on Juri/Haruka or even a way of clearing obstacles between himself and Juri and not just because he wanted to revive Kaname the Ancestor. The second attempt with Yuki could therefore, be seen as another attempt of him getting revenge etc. However, after finally seeing Yuki in the 42nd Night, and realizing that they are incredibly alike, that would have unearthed his obsession for Juri to the point that he believed Yuki to be Juri and subsequently, creating an obsession with Yuki. This is a pretty drastic change from wanting to kill Yuki to wanting to love her and also shows that Rido was simply heartbroken and needing to cling onto anything that resembles Juri who was unfortunately Yuki. Despite all of this, Yuki only shows minimal resentment to Rido because of the fact that he killed her family.