Mermaid Saga

This is Rumiko Takahashi at her darkest, but her trademark humor and romance also pop up in this three-volume series. Legend has it that if a human eats a mermaid's flesh, they will be granted eternal life. But is that a blessing or a curse? Immortal lovers Yuta and Mana travel through Japan and the centuries longing for a normal life. On their journey, they meet others who have consumed the flesh of a mermaid in hope of becoming immortal. But the powerful substance affects each person differently. Yuta and Mana are two of the lucky ones. Others are fated to die or transform into a savage monster, a "lost soul." 

(Source: VIZ Media) 

*Note: This is the first volume of the Mermaid Saga series from the original tankoubon release, which includes the two-chapter stories "A Mermaid Never Smiles" (人魚は笑わない, Ningyo wa Warawanai), "The Village of Fighting Fish" (闘魚の里, Tōgyo no Sato), and "Mermaid Forest" (人魚の森, Ningyo no Mori Zenpen).*