Short answers, pulled from the story.
Shaivism is an umbrella term for Hindu religious traditions that worship Shiva as the supreme being. It has approximately 385 million followers, concentrated primarily in India, Sri Lanka, and Nepal.
The earliest traceable root of Shaivism is the worship of the Vedic deity Rudra, mentioned in the Rigveda (roughly 1500-1200 BCE). According to Gavin Flood, the formation of Shaiva traditions as we understand them began to occur during the period from 200 BCE to 100 CE. The earliest unambiguous sectarian evidence appears with the Pashupata in the early centuries of the common era.
Shaivism encompasses Puranic Shaivism (a householder religion revering the Vedas and Puranas), and non-Puranic or Agamic Shaivism, which divides into the atimarga (path for renunciates only) and the mantramarga (open to monks and householders). Major sub-traditions include the Pashupata, Lakula, Shaiva Siddhanta, Kashmir Shaivism, the Kapalika, the Nath tradition, and Lingayatism.
Lingayatism was founded by the 12th-century philosopher and statesman Basava and spread by his followers called Sharanas. It emphasises qualified monism and loving devotion (bhakti) to Shiva, and its scripture the Basava Purana was completed in 1369 during the reign of the Vijayanagara ruler Bukka Raya I.
Shaivism arrived in Southeast Asia from South India in the early 1st millennium CE, co-developing with Buddhism across the region. Temple archaeology and inscriptions from Indonesia dated 400-700 CE indicate Shiva was regarded as the highest god. The tradition built thousands of temples across the islands of Indonesia as well as in Cambodia and Vietnam, and it persists today in the province of Bali.
Shaivism has been a major innovator in yoga. The Shiva Sutras teach yoga in many forms, and the tradition's central premise is that yoga means realising one's true inherent nature as identical with Shiva. The Nath Yogis, founded by Matsyendranath and developed by Gorakshanath, integrated Hatha Yoga techniques and went on to influence 18th-century Advaita Vedanta.