The term Hindu came into existence from Indus River. It means to the communities that live close to Indus River (area in modern Pakistan).
People of Harappa who used to live nearby Indus River around 2500 BC carved several images of various gods on clay seals. It is not yet revealed what Harappans addressed their gods because we can’t understand their written evidences. We are not familiar with their written language. However, some of their gods look like Hindu gods Vishnu and Shiva. So, this might be the sign of Hinduism in this part of the world.
Invade of Aryan
Around 1500 BC, Indo-Europeans (Aryans) invaded to India. Along with them, they brought their culture and sky gods. After the mixture of two cultures, Indians started speaking Hindi. Consequently, Hinduism got new thoughts and new gods.
One of the ancient evidences about Hinduism is Rig Veda. It has a collection of various Hindu poems in Sanskrit composed around 1000 BC. Indians recited and sang Rig Veda for many years. Rig Veda includes a number of magic spells, hymns, and instructions that are said while sacrificing any animal.
Rig Veda beliefs in polytheism i.e. about multiple gods. Mostly supernatural beings (gods) are male like weather gods and sky gods such as Indra, and god of sea Varuna. Inhabitants sacrificed different animals to gods. Rig Veda tells that at times people get in touch with gods and talk to them. Agni (fire) and Soma (ritual drink) were worshiped as gods.
Around 600 BC, the thought of reincarnation got well-known among Hindus. They started thinking that after their death they would reborn in a new body. If they were involved in virtues as per Dharma (Hindu deity), then they would get an extraordinary body such as prince or princess. On the other hand, if they had done sins, they would get an animal/insect body like rat or cockroach.
Gradually, Hindus started to hate the rebirth idea. They wanted to get rid of this endless reincarnation. They thought that sacrificing animals was a sin as per their Karma (fate). Thereafter, the process of sacrificing animals became lesser in different parts of India.
Around 300 BC, Hindus began worshiping new gods and they did not require animal sacrifice. Some of the new gods were Shiva and Vishnu. Devotees commonly gave Shiva and Vishnu fruit, flowers, prayers or incense, and did not like to sacrifice animals. They started paying more attention to Shiva and Vishnu instead of old gods like Varuna and Indra.
Later on between 400 AD and 650 AD, after the end of Gupta period, a new goodness arrived into Hinduism. She was Mother Goddess. The Mother Goddess had a sacred animal viz. cow, hence Hindus stopped consuming beef.
Similar to Shiva and Vishnu, Mother Goddess had so many Avatars (incarnations). Her incarnations like Annapurna, Uma and Parvati were beautiful but others like Chamunda, Kali, Durga and Chandi were giants.