The Anti-Hero could be defined as an lead character, often as a presumptive hero, who does not possess heroic qualities. He or she is not courageous or noble or moral, the goal for them is survival or some other selfish target. They are possessed of ambiguous morality, often being as flawed, or frankly, evil as the antagonist they fight. The role they play is an archetype of hero, that is turned upside down. In some cases this is meant to be a means to expose the ultimate human foundation of any "hero" but sometimes it is just a means to tell a story. The lack of moral tone can be attractive to some readers, who tire of the hero being ever so good.
The character was painted into existence by Frank Frazetta and was seen fighting bad guys, but, his red glowing eyes and menacing look, let you imagine, he was more pissed than being heroic. James R. Silke was one of the first to bring Death Dealer's tales to life in story. And the stories are vivid, wildly entertaining and well written. I would hesitate to call Death Dealer an anti hero, in that the helmet is the cause of his actions. He is Gath of Baal, and wears a cursed helmet that makes him the bearer of the form of the God of Death. His actions, thereby, are not his own. We see him taking many lives, and not many good people dying by his hand. These books were well written and I recommend them, but they are hard to find and expensive. So happy hunting.
Michael Moorcock is a very bright writer who writes stories to examine the motives and weaknesses of his lead character, Elric of Melnibone. He is an elf or elf like Emperor of an ancient people and land, and his sorcery and skill in battle are augmented by his resort to calling upon evil Gods, elementals of power, and an unique sword that drains souls. He is described as a weak, pale albino, with deeply introspective fears and wonders. He is selfish, and hateful. But, he is also a creature of his time and people, so, at some points he is kind, he is capable of love, and he is also seemingly cursed. These books have been collected in many forms, I love those shown below, with Michael Whelan covers.
Karl Edward Wagner wrote numerous tales, edited some works by greats, such as Robert E. Howard, and his most acclaimed work surrounds his Anti Hero, Kane. The attraction to the character Kane is rather the opposite of what was just said about Elric. Kane is handsome, powerful, brilliant, and he is curious, and that makes him try to find powerful items to make him more able, in his quest to become the most powerful man upon the planet. He doesn't suffer from weakness, he is powerful in sorcery, swordplay, and darker arts of magic. Wagner wasn't, apparently, interested in telling the stories to follow a weak young man into a powerful older king. He was showing the reader the mind of one who was powerful, and wanted more power.
John Norman in his real life was a professor of philosophy. He wrote the counter Earth planet Gor into life with the adventures of Earth man Tarl Cabot. Cabot was initially horrified to see humans used as slaves, and violence and ancient codes of honor ruling the planet. But eventually, after a time spent becoming Gorean, he too adopts the practices. The later books of the series become more explicit in slavery, sexual domination, and cruelty. The author has said that Gor is a place that the theories of Nietzsche and Freud are played out. The strong rule the weak, and sex becomes a highly ritualized form of exchange of power.