From a writer's perspective, one of the characters in fiction I find most interesting is Jaime Lannister.

The reason is that the story immediately puts him past the moral event horizon, but then *still* gets you to kind of like him. That's really hard.

I'll focus on the show rather than the books. In the first episode of the show, he pushes a child out of a window to their near-fatal death. Jaime is royalty, and he's an asshole, and the kid did nothing wrong. And he's casual about killing a child. There's nothing more bad than that, so we hate him immediately. Enemy #1.

So the narrative starts in hard mode. How to make this character semi-likeable. What made him do such a crazy thing.

Jaime loves his sister. At first that's another red flag. We almost all cringe at incest. An incestual killer is like bottom-of-the-barrel, almost comically bad. But... they're legit in love and have c hildren. The kid saw them together, and Jamie tried to kill the kid to preserve the secret.

So as an audience we're like, "Well, fuck, okay this is a medieval England/Westeros world where almost everyone is dirty, and his own royal sister is the hottest person to him, and they fell in love." It's not like they have the Internet to keep them entertained and knowledgeable; these things could happen in their palace. They had children, and now are in a tough position, since the sister is married to the king and are assumed to be his heirs but are really Jaime's. They can never say they this to anyone, because both they and the children would be killed. So regardless of what one may think about the young versions of them that got into this mess, once they are in this mess as adults, the audience is kind of like, "well, who wouldn't take extreme action for their own kids if it came down to it, especially in such a brutal world?"

Jaime then becomes an understandable villain. We hate him, but we understand him. He's not evily twirling his mustaches for no reason; he's dealing with a chain of events that started when he was young.

And then over time, the narrative crosses the bridge into actual likeability. He loses a war, he gets captured, he gets humbled and has a rough time. And he's a charismatic top-tier swordsman.

We also learn more about his backstory. He was a kings' guard that killed the king, which gives him widespread dishonor. But the king was a monster, and he killed him for good reasons. So, that's interesting. Even people who disliked that king tend to dislike Jaime since his action was so dishonorable ("one does not kill the king they guard, even if the king is bad"), whereas Jaime has more of the pragmatic anti-honor approach of "Well, he was fucking bad, though. I had to."

He then escapes with Brienne of Tarth, which has a typical buddy-cop narrative or fantasy guy/girl semi-romance narrative, since they don't like each other but then eventually grow to like each other amid their travels. And then he gets his hand cut off, which in addition to being painful attacks his main attribute (top-tier swordsman) and humbles him. He also does his best to keep Brienne safe, since he grows to respect her and even maybe love her. We see his good side. We almost see him as a boy in this arc, just some guy who we feel bad for and is kind of simple and meaning to do well.

And from then til the end, he's always a more likable character. Most readers and audience members find themselves generally on Jaime's side. An anti-hero, who once pushed a kid out of a window.