Celebrating the Diwali festival
The word Hindu comes from the river Indus, and it just means the people who live near the Indus river (actually in modern Pakistan).
The Harappa people who lived near that river about 2500 BC carved images of several different gods on their clay seals. We can't read Harappan writing, so we don't know what the Harappan people called their gods. But some of these gods look a lot like the later Hindu gods Shiva and Vishnu, so this may be the earliest part of Hinduism.
About 1500 BC, when the Indo-Europeans invaded India, they brought with them their Indo-European sky gods. The two cultures mixed, and people in India began speaking Hindi, an Indo-European language. So their gods mixed too. Hinduism got some new gods, and also some new ideas.
The first written evidence of Hinduism that we can read is the Rig Veda, a long poem in Sanskrit probably composed about 1000 BC. People sang or recited the Rig Veda for hundreds of years before it was written down around 300 BC, when Indian people learned about the alphabet, during the Mauryan Empire. The Rig Veda is a bunch of hymns (HIMS) (songs for the gods), magic spells, and instructions for what to say when you are sacrificing animals.
The Rig Veda mentions many different gods (polytheism). Most of the gods are male, and many of them are sky gods or weather gods like Indra, the god of rain, or Varuna, the god of the sea. People sacrificed goats and chickens to their gods. The Rig Veda also tells us that people sometimes got in touch with the gods by using a drug, soma, which made them hear the gods talking to them. (We don't know now what soma was made of). Both soma and the fire of sacrifice (Agni) were thought of as gods themselves, too.
About 600 BC, the idea of reincarnation became more and more common among Hindus. Most people began to think that after you died you would be reborn into another body. If you had been good, and lived in accordance with dharma, you would get a good body, maybe a princess. If you had been bad, and piled up a lot of karma, you would come back as a cockroach or a rat.
Gradually people began to hate the idea that you had to be endlessly reborn in different forms. They wanted to get free of the wheel of rebirth, and just be left alone in Nirvana. People began to think that sacrificing animals was a burden on your karma, or fate, that prevented you from getting free of reincarnation. So animal sacrifice became less popular.
Kali (from Kalinga in Eastern
India, about 1000 AD)
Around 300 BC, the Mauryan Empire united India and the Silk Road increased trade. People began to worship new gods, who didn't need animal sacrifices. These new gods were Brahma, Vishnu and Shiva. Generally people gave Vishnu and Shiva flowers, incense, prayers, fruit, or music, but they didn't kill animals for them. They began to worship Brahma, Vishnu, and Shiva more, and paid less attention to their old gods Indra and Varuna and the others. One example where they're sacrificing fruit is the story of how Ganesh cursed the moon.
Much later, between 400 and 650 AD, at the end of the Gupta period, another new god came into Hinduism. This new god was a Mother Goddess. Cows were sacred to this Mother Goddess, and so Hindus gradually stopped eating beef. Like Vishnu and Shiva, the Mother Goddess had many incarnations and many names. Parvati, Uma, and Annapurna were beautiful goddesses, who brought blessings to people. But other incarnations were called Kali, Chandi, Durga or Chamunda, and these goddesses were terrible giants with black skin, huge red tongues that stick out, and fierce tusks. These had many arms and each arm held a weapon, and they wore necklaces of skulls or human heads.