Inu Yasha is a hanyou, half dog demon, half human, living in feudal Japan.  At the begining of the story, Kagome finds him bound to a tree by an arrow, the same tree he has been stuck to for fifty years.  Ever since his old love, Kikyou, bound him there with her dying actions.  Being only half demon, he is accepted by neither humans nor demons and has had a hard life so far.  Kaede, Kikyou's little sister, puts the rosary around Inu Yasha's neck when Kagome unbinds him from the tree.  The rosary has a spell attached to it, linked to Kagome.  Basically, whenever Kagome says 'sit' (oswari), Inu Yasha is pulled, face first, into the dirt.  This gives Kagome control over him and allows the two to work together to find the shards of the Shikon no tama, a jewel that Kikyou guarded while alive and was inside of Kagome when she was born.
Kagome is a young girl from modern day Japan.  She grew up at a shrine, run by her grandfather.  One day, Kagome was dragged into a well at the shrine by a demon.  The demon's bones had been at the bottom of the well, and the demon, sensing the shikon no tama inside of Kagome which increased demon's power, had reawakened.  When Kagome fell through the well, she also fell through time and came out in the feudal age of Japan.  After freeing Inu Yasha from the god tree where he was bound, the shikon no tama was stolen by a crow demon.  As it was flying away, Kagome launched an arrow after it which struck the jewel, shattering it into an unknown number of shards which reigned down all over.  Kaede, an elderly miko, or priestess, convinced Kagome and Inu Yasha that they had to work together to find and recover all the jewel shards.  For Inu Yasha had the strength to fight the demons who wanted the jewels power and Kagome was able to sense where the shards were located.  While this is not always a peaceful or happy partnership, the two have a rough friendship and soon travel together more because they want to than because they have to.  Kagome is able to return to her own time whenever she pleases through the bone eaters well.  So far, only Inu Yasha has been able to follow her to her own time, usually to fetch her when she is taking too long to return to their quest because of school.
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