Hinduism or Hindu Dharma is a very vast and old religion with an unknown antiquity and origin, perhaps the oldest in the world. Within itself it encompasses the core features of almost all other religions found in this world, including atheism. The traditional Hindus don't call this religion Hinduism, rather they prefer calling it "Sanatana Dharma" or the "Eternal Way of Life". Hinduism has no founder, no religious head, not specific set of rules for all, no fixed beliefs to be adhered too. Anyone can follow anything and yet call himself a Hindu. Hinduism allows questioning all of its basic tenets.
Hinduism can be broadly classified as orthodox and hetrodox. Within each of these classifications there are thousand other beliefs, sects, divisions, schools of philosophy and many other things. Hinduism believes in the concept that all beings are equal. Though various schools differ on this, but all of them accept that the same soul resides everywhere, including in non-sentient things. One great aspect of Hinduism is tolerance which has no parallels in any other religions of the world. Which ever religion came into contact with Hinduism, Hinduism absorbed it, apart from that its flexibility to question itself allowed several other religious schools like buddhism, jainism and sikhism among others to sprang up.
Hinduism is mainly followed in India and Nepal. For several millenia the hindu religion has shaped and influenced the thinking of the people following it. It also fostered scientific and philosophical thinking as evidenced by its vast collection of literature. Hindu literature starts with earliest text knows as Vedas (which are considered Indo-European in origin). Vedas are still the oldest known available Indo-European texts.
As mentioned earlier, Hinduism has a vast literature and much of it is written in an ancient language called Sanskrit, the first reference of this language comes from the Vedas, though the grammar and language style used there is different, but the same vedic sanskrit evolved into later day classical sanskrit.
Hinduism, being a term coined by Western scholars which lumps together many different Vedic religions, is not considered culturally sensitive among many groups, such as some within Vaishnavism who do not appreciate being called Hindu.
Also visit Nonkilling in Hinduism at the School of Nonkilling Studies.