Do you mean Hinduism the word, or Hinduism the religion? Carl Olson's The Many Colors of Hinduism: A Thematic-Historical Introduction is a really excellent introduction to everything having to do with Hinduism, and it's accessible as well if you'd ever like to read it. According to Olson, the term "Hindu" was used by Muslims entering the Indus valley in the eighth century. Later it was used to distinguish between indigenous peoples and Muslims. The term "Hinduism" was used by non-Indians (especially the British) as an umbrella term that described a variety of different religious ideas, texts, and practices.

So to use this umbrella term, Hinduism the religion originated in India, and that's about all anyone can agree on. Some scholars say it began in the Indus Valley/Harappa civilization, while others say it came from the Indo-Aryan civilization which emerged after Aryan immigrants conquered the indigenous Harappa culture. The earliest religious "texts" (put in quotes because they originated as oral poems) were hymns of praise to gods and leaders called the Vedas, which originated in northern India around 1500 BCE. I hope this was helpful!