After Alexander went back to Babylon in 324 BC, a man named Chandragupta was able to overthrow the old Vedic kingdom of Nanda and form a big new empire over all of northern India and into Afghanistan. Greek historians said that Chandragupta got the idea from Alexander. But it seems more likely that, like Alexander, the Indians got the idea of forming empires from the Persians, or just from earlier Vedic empire-builders in India. Chandragupta conquered the Indus valley back from the Greeks and as part of the peace treaty he married the daughter of Seleucus, who had succeeded Alexander, and gave Seleucus 200 elephants.
A coin of Ashoka
Chandragupta died in 298 BC and was succeeded by his son Bindusara. Bindusara's son Ashoka made the Mauryan Empire even stronger, ruling some of southern India as well as the north.
But Ashoka's victories at Orissa were so bloody and awful, that (at least according to tradition) after that battle he gave up warfare for the rest of his life. Ashoka converted from traditional Indian Hinduism to the new faith of Buddhism, and he used his power to convince millions of other people to convert to Buddhism too, all over Central Asia.
After Ashoka died in 231 BC, though, his sons and grandsons were not as strong rulers as he was, and the Mauryan Empire gradually fell apart.
To find out more about the Mauryan Empire, check out these books from Amazon or from your local library:
Note: The first of these is a comic book, but it's a good story!