Inuyasha is named after its hero, a half-demon-dog, half-human boy (?) who looks a lot like any other manga-style half-demon-dog, half-human boy: he has slitted pupils, long fingernails, long (white) hair, and sharp pointy doggy ears; and aside from this, is young and handsome (of course). But the main character is actually Kagome, a fifteen-year-old schoolgirl from modern-day Japan. She, like any other manga-style girl, is tall, slender, and in this case has long black hair (and of course is cute).
The series started with Inuyasha attempting to steal a mysterious magical jewel called the Shikon No Tama from a burning village. He was, however, nailed to a tree by an arrow shot by a young woman shaman named Kikyou. Kikyou, dying from heavy wounds, took back the Shikon No Tama and was later cremated with it. The dead or unconscious Inuyasha, meanwhile, was bound magically to the tree for fifty long years....
In modern day Japan, young Kagome is pulled (by a monster, of course) into an old dry well on her family's temple property. Expectedly, she finds herself in 15th or 16th-century Japan, in the midst of its civil war era. Her arrival awakens Inuyasha from his fifty-year nap. He turns out to be a rude, condescending, greedy boy who wants nothing more than the Shikon No Tama, which grants incredible power to evil creatures. Naturally, other monsters want the Shikon No Tama, too --- which has reappeared with Kagome's arrival.
Inuyasha finds himself helping Kagome against greedy monsters, almost unwillingly; and in one terrible conflict, the two wind up shattering the Shikon No Tama into shards that fly across the land. With the help of Kikyou's younger sister Kaede (now an old woman), they determine that (1) Kagome is likely the reincarnation of Kikyou (she even looks exactly like Kikyou) (2) Kagome and Inuyasha need to retrieve the fragments together, before too many evil monsters become too powerful.
Inuyasha isn't happy about this partnership and quest, but is gradually convinced. He wants the Shikon No Tama for himself, after all, and he realizes he needs Kagome's sixth sense to find it. Early on, however, Inuyasha poses quite a threat to Kagome. Fortunately, Kaede outfits Inuyasha with a magical collar that instantly flattens him when Kagome tells him to "Sit!" ... he is part demon-dog after all.
Now teamed up, Kagome and Inuyasha travel the lands, seeking the fragments of the Shikon No Tama (whose history has never been fully explained). This means they must hunt down and defeat monsters that have taken up the fragments --- and they must fend off monsters that are seeking the fragments they hold. They also run into plenty of unrelated creatures and monsters on the side, in both old Japan and modern Japan (where Kagome also has to struggle to keep up in school); once or twice they even pick up a long-term ally or friend, from Old Myoga the Louse to Shippou the young fox.
That's the basic premise of the story. The episodes themselves are fast-paced, well-laid-out with good flow (Takahashi is brilliant at this), combining humor, horror, and plenty of both action and quiet moments of rest. The mood is distinctly darker than in Ranma (though probably lighter than that of the Mermaid stories), and the monsters do actually kill people.
The characters are a nice change from the previous long-running series, too. Kagome and Inuyash form a dynamic pair that is far more peaceful and cooperative than Ranma-Akane or Lum-Ataru, but is still conveniently prone to letting pride and panic disrupt what might otherwise turn into intimate moments (after all, the romance can't be allowed to develop too quickly). Inuyasha's gradual and continuing growth into a caring young man has been well-done and convincing (though of course he is nowhere near being polite yet). Kagome, despite being the main character, hasn't changed very much; she is a friendly, caring, and brave girl refreshingly not prone to fits of pride (unlike Akane). Unlike Lum or Akane, she also has no battle powers, but her insights and brilliant ideas save their lives nearly as often as Inuyasha's superhuman powers.
And unlike Ranma and Akane, many questions remain about both Inuyasha and Kagome. A late 1997 story addressed some of them, showing glimpses of Inuyasha's tragic relationship with Kikyou. What happened the fateful day the dying Kikyou shot Inuyasha and bound him to a tree? The story is fraught with betrayal and mystery. It is not even clear that Kagome is a mere reincarnation of Kikyou; she may be something else, or something more. (Early 1998 has yielded only a few answers: there is a mysterious shapeshifter who is after the Shikon No Tama, who apparently smells of ink. But there is a new question: what has become of Kikyou's resurrected body, now inhabited by an anguished, vengeful fragment of her soul?)
And then there's Inuyasha's physiology. What is it that happens to Inuyasha at certain times of the month, when his body changes shape? Will Inuyasha, though intent on becoming a full-fledged monster, one day become human instead? (Well, OK, I admit that question was very similar to "Will Ranma ever stop turning into a girl?") And (again) what of Kagome? Is she really Kikyou's reincarnated soul? Why was the Shikon No Tama hidden in her body?
There are sillier questions, too. What happens to the modern-day school boy who is desperately trying to win Kagome's attention? Will Kagome manage to pass her math class when she's gone most of the time? Does Buyo the fat and lazy cat have any bones in his body?
So far, I think I like this better than Ranma 1/2. A distinctly worthy read for fans of Takahashi Rumiko, so long as constant gag comedy-humor isn't expected. (And, according to a January '98 Shonen Sunday, 88% of junior high school girls read Inuyasha ... now that's popularity!)
BTW, I provide frequent updates on Inuyasha in the Shonen Sunday review section of EX Magazine. Here is my Inuyasha Volume 2 Review.
As a last note, any manga scholars may wish to contrast this series to the Tezuka Osamu manga Dororo from roughly 1969, in which an unusual young man and his small thiefly sidekick are seeking out and destroying 48(?) demons throughout old Japan.