First Appearance.
In Arkham Knight, he is kidnapped and tortured for years but not killed. Instead he is mentally abused and made to believe Batman is the source of his suffering. In Arkham Knight, he is starved and beaten, by Joker and by others sometimes dressed up as Batman.
In the post-Crisis DC Universe, Jason Todd was tortured and killed by The Joker in the infamous “A Death in the Family” storyline, and while Todd has been resurrected since then, it remains one of the Dark Knight's most tragic moments (and one of The Joker's cruelest).
Soon after, spurring on by the anti-fear gas, Jason confronts Joker and dies. Death, though, isn't exactly a permanent state in comics. Jason's body is soon taken to a Lazarus Pit left by Ra's al Ghul and dunked inside. Thanks to the healing properties of the Lazarus Pit, Jason is restored to life.
He used Jason's mom as bait. Jason found out the woman he thought was his mom was actually his stepmom, so he went on a search for her. He thought he was an orphan up to this point, and the thought of finding her consumed him. Batman was investigating a crime by the Joker, and bumped into Jason.
There, with Frank Boles covering for him, Joker tortured and brainwashed the young man. As part of a psychological plan, Joker forced Jason into believing that Batman had abandoned him, and that Batman was the true villain. That would lead to a future confrontation between mentor and ward that would break Batman.
edit: now i believe he was 15 or 16 years old, no more and no less, that's the age of the trigger for puberty and at that age he builds the muscle mass he had in the movie. Edit2: Did you guys realize how cruel the Joker is? He tortured an underage teenager to death!
Despite the violence of the beating, Jason spares Joker, intending to use him later against Batman. Jason Todd, revealed himself being alive and as the Red Hood to the stunned Joker, after he pummeled him with a crowbar, in Batman #638.
However, he somehow popped up in one piece back at Crystal Lake at the start of Part IX. Then he was blown to bits, although his heart continued to beat. The living heart allowed him to possess living humans. Then we learn Jason can be born again through another Voorhees, and that only a Voorhees can kill him forever.
If Jason Todd had the opportunity, would he still kill the Joker? No, while Jason is still haunted by the past, he doesn't want to kill the Joker anymore. Jason said that he can't kill the Joker because he lives in his memories and for the Joker to die he would need to forget what happened to him.
The most common story involves him falling into a tank of chemical waste that bleaches his skin white and turns his hair green and lips bright red; the resulting disfigurement drives him insane. The antithesis of Batman in personality and appearance, the Joker is considered by critics to be his perfect adversary.
Jason chose to take over the moniker so he could own what the Joker did to him and use it to become the Joker's destruction. This set the Red Hood on a path to become a brooding, bitter anti-hero who often crosses lines that others in the Bat-family won't.
The final betrayal comes from Medea herself, who not only kills Glauce and Glauce's father, but also kills her and Jason's two sons. This is not only a betrayal to Jason, but it's also a betrayal of her two boys.
TLDR: Superman didn't save Jason because he was being tortured by Lex Luthor at the time in order for Luthor to create Conner Kent/Superboy. This is why he wants nothing to do with Superboy once he appears.
A Death in the Bat-Family
That's easy, you kill Robin! “A Death in the Family,” which ran in Batman #426-429, hinges on a chilling scene where the Joker ambushes Robin (Jason Todd) and beats the Boy Wonder senseless with a crowbar, leaving him tied up in a warehouse with a bomb.
Jason remained dead for six months, his legacy haunting Batman. However, when the evil-alternate reality Superman known as Superboy-Prime punched reality itself, the timeline stuttered, and Jason was restored to life. Jason broke out of his coffin, but collapsed from exhaustion in the cemetery.
Jason was rendered mute after barely surviving his near drowning at the age of 11. He was slightly mentally challenged before then and the fact that he was abused by the other campers made it worse. As shown in flashbacks during Freddy vs.
Jason begins killing those who occupy Crystal Lake, and after a battle with Tina, is dragged back to the bottom of the lake by an apparition of Tina's father. Friday the 13th Part VIII: Jason Takes Manhattan (1989) sees Jason return from the grave, brought back to life via an underwater electrical cable.
Michael Myers could not die in the earlier films because The Cult of Thorn has cursed children from his tribe, rendering them “immortal.” They also commanded him to murder every family member as a sacrifice to maintain the cult members' immortality. This supernatural power was even hinted at during the recent trilogy.
The Joker murdered Jason, the second Robin, back in the 1988 Batman story arc "A Death in the Family." Jason did not stay dead, however, and was later resurrected thanks to some Multiverse-shattering events and a dip in one of Ra's al Ghul's Lazarus Pits, allowing for his transformation into the gun-toting vigilante, ...
In the story, the Joker takes Harleen Quinzel to the chemical plant where he originated and pushes her into a vat of chemicals against her will, which bleaches her skin and drives her insane, resulting in her transformation to Harley Quinn, similar to the Joker's transformation in his origins.
Dick Grayson, the original Robin, gets word that Batman snapped and killed the Joker. He goes back to Gotham to confirm this, and sees the body himself. It's just a mangled corpse out of view, but fans know the green hair anywhere.
Seeing Jason as he was back then though, would have overwhelmed Batman with guilt and shame, perhaps even convincing him to retire as a hero entirely. This in turn showcases that Batman prioritized his own needs over Jason's. He knew that he could have helped his son, but he chose not to because it was easier.
Red Hood (real name Jason Peter Todd) is a fictional character and a major anti-hero from DC comics, appearing as a major character and vigilante from Batman's corner of the DC Universe.
On Earth- 51, Batman went on to kill the Joker after Jason Todd's death and eventually killed off a majority of his world's Supervillains in ways that looked like accidents. Because he was never caught, he simply went into semi retirement along with the majority of his world's heroes.