Rumiko Takahashi is a long-standing mangaka, most well known these days of Inu Yasha, Ranma 1/2 and Urusei Yatura. She's incredibly prolific, easily capable of churning out books by the dozen, but while more often than not her titles start out strongly, after 15 or so volumes they start to run out of steam and recycle to same jokes and ideas.
Mermaid Saga is comparatively short at 4 volumes, so though not wanting to venture 50+ volumes of Inu Yasha, but still wanting their Takahashi-styled supernatural/monster fix would do very well to check this out.
Centering on the premise that eating the flesh of a Mermaid will make you immortal, the series follows a young-appearing couple who have notched a fair few hundred years between them while investigating rumours surrounding the mermaid in hopes of escaping its curse. The promise of immortality is always prone to attract the worst sort of people, so it's no surprise that a steady line of nutjobs are after it and will take anyone who gets in their way. Ranma never had to deal with having one of his eyes gouged out, but this is the level of nastiness that Takahashi introduces here which may surprise fans of her lighter work. The violence is ugly with many of the characters being irredeemable obsessives. It makes for gripping reading and its short length means it doesn't outstay its welcome.
It's a short and sweet entry in Takahashi's works, and one I'd put as being essential reading alongside Maison Ikkoku (trust me, it's really good). Hardcore fans can dive right into her more epic works, but for sampling her more interesting and intense work, I'd go for this one.