Inuyasha, a Hanyou, is a character who doesn't show his emotions often. He's very powerful and somewhat smug. Also a very bad-mouthed person, he usually doesn't think things through. Inuyasha isn't accepted by humans and youkai, being half of each and all. He was made fun of by the youkai, and feared by the humans. Since then, he was wary of the people he chose to trust.
In the past, he was in love with Kikyou, and then he met Kagome. He's confused with them both, and doesn't know who to get with. He gives onlookers the impression that he is with them both. He cares a great deal for Kagome, and uses his powers to protect her in the series. He cares for her so much, that when she has to return often back to her time period (this is to prevent suspicion from her disappearence) he doesn't really do much but sulk. The weird thing is that with Kagome around, he seems more powerful.
Though Inuyasha's true age is never revealed, Rumiko Takahashi states that Inuyasha has the mindset of a seventeen year old, though he's obviously many, many years older since he was sealed to a tree for fifty years and seeing how youkai don't age at the same rates as Humans, Inuyasha could easily be over a hundred years old.