Inuyasha ("dog demon" in Japanese) was a hugely popular Manga (comic book) and Anime series in Japan. The series written and illustrated by Rumiko Takahashi. The story begins in Tokyo, Japan, with a fifteen-year-old middle school girl named Kagome Higurashi, who lives on the grounds of her family's hereditary Shinto shrine. When she goes into the well house to retrieve her cat, Buyo, a centipede demon bursts out of the enshrined Bone Eater's Well and pulls her through it. As she leaves the well, Kagome appears in the ancient Sengoku period of Japan. During the demon's previous attack, a magical jewel known as the Sacred Jewel of Four Souls (Shikon no tama) was embodied from Kagome. She then becomes the demon's target and it tries to consume the Jewel and kill Kagome. In desperation, Kagome unseals the half-dog demon, half-human InuYasha who was placed on a tree fifty years ago by Kagome's incarnation Kikyo, the young miko of the village in charge of the Sacred Jewel who had, upon her death, requested that the Jewel be burned in her funeral pyre so no one could ever abuse its tremendous power. Although InuYasha destroys the centipede, the Sacred Jewel is later shattered into numerous shards that disperse across Japan. Even the individual shards are capable of granting great power of the whole entire Jewel, and are eagerly sought by humans and demons alike. InuYasha and Kagome set out to collect the shards to avoid disasters caused by the Sacred Jewel of Four Souls.
Presenting here the very first episode for you to watch. If you like it, I am sure you can find various websites that feature this Anime, however be warned, unlike most Anime, that run for 24-28 episodes this ran for a few years.