Now, you might be wondering how Jason Todd, one of the most permanently dead of all comic book characters, got himself resurrected.
Blame the seed of the idea on Batman: Hush (which is a great storyline, but there's always a catch, right?). In that story, Hush and the Riddler are carrying out a campaign of psychological torture on Batman, so they hire Clayface to impersonate Jason Todd under the Hush mask and confront Batman. The two battle, and all the while Todd is blaming Batman for getting him killed and saying every bitter, hurtful thing that comes to mind. Batman, being the world's greatest detective, is not fooled, and figures out that it's not really Jason Todd.
But the scene was really cool. It looked cool, and it was a bold idea. Of course, most people who read it probably wanted to let it lie and not develop the idea of Jason Todd actually coming back.
But then, most people aren't talentless hack writers like Judd Winick. Judd thought it was an AWESOME idea, because he has little respect for the history of the characters he writes.
So later, Batman finds that Jason Todd's grave is empty. At first it looks like the Riddler stole the body just to mess with Batman some more. But then it turns out that it all ties into Identity Crisis.
I won't go too far into that whole convoluted mess, so just go with me here. An alternate universe Superboy was trapped in an extradimensional space, and, using his boosted powers, started pounding on the 'walls' of his prison with his fists. These impacts sent something akin to quantum shockwaves through all levels of reality, thus reversing some historical events and making other events completely altered in a weird way.
So basically, Jason Todd came back to life because alternate universe Superbody hit reality so hard that it skipped like an old television, and changed history around in such a way that Todd sat up in his coffin and went on a vigilante spree. I love comic books, don't you?
About the 'Red Hood' identity: the Joker's origin story (and take it with a grain of salt, since he's the one that tells it, and he's insane) is that the Joker wore a red hood when he broke into Axis Chemicals and was knocked into that chemical vat by Batman. So the "red hood" was Joker's first costumed identity, back when he was a mobster thug in way over his head. In fact, it was the presence of the hood on his head that led in part to his facial disfigurations (the hood held the chemicals against his face longer than the rest of his body).
So, Jason Todd comes back to life, and has a mad-on for getting back at the Joker, the guy who murdered him. In order to rub salt in the wound, Todd claims the Joker's old identity. It's all about psychological warfare these days.
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