Shaivism is the worship of Shiva as the supreme reality, and its distinguishing quality is a persistent tension with the ordinary religious order.
Shiva is the god of the margins: the ascetic on the cremation ground, smeared with ash, outside caste and outside the settled world of sacrifice and household duty. The traditions built around him have repeatedly taken that seriously in practice, producing renunciate orders, tantric lineages working deliberately with what other Hindus regard as polluting, and reform movements that rejected caste and the Brahminical priesthood outright. Shaivism also produced the most rigorous non-dual philosophy in India outside Advaita Vedanta. It is not one thing, and the entry that treats it as one thing will be wrong.
Its origins are argued over and frequently overstated. The seal from Mohenjo-daro conventionally called Pashupati, showing a horned seated figure, is regularly presented as evidence of Shiva worship in the Indus valley four and a half thousand years ago. Gavin Flood describes such readings as speculative, and this atlas does not carry the claim as established.
The clear textual antecedent is the Vedic Rudra, the dangerous outsider god of the Rigveda, addressed with a care that reads as wariness. The formation of Shaiva traditions as such, on Flood's account and the mainstream one, happens between about 200 BCE and 100 CE, with the Pashupata ascetics as the earliest identifiable sectarian movement, a group whose observances were designed, on their own account, to attract public contempt.