Some of the best entry-level anime series for someone new to anime are:
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My Hero Academia: A story about a boy born without superpowers in a world where they are the norm, but who still dreams of becoming a hero.
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Attack on Titan: Follows the story of humanity's fight for survival against giant humanoid creatures known as Titans.
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One Punch Man: Follows the story of Saitama, a hero who can defeat any opponent with a single punch, leading to his boredom and search for a worthy opponent.
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Death Note: Focuses on a high school student who gains a notebook that allows him to kill anyone by writing their name in it, and the cat-and-mouse game with a genius detective trying to stop him.
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Fullmetal Alchemist: Brotherhood: Follows two brothers who use alchemy in their quest to find the Philosopher's Stone and restore their bodies after a failed alchemical ritual.
These series are popular among both new and seasoned anime viewers and offer a good introduction to the various genres and storytelling styles found in anime.