Asoka (272-231 BC), grandson of Chandragupta, founded the first Indian empire, including all of modern India except the southern tip, plus Pakistan, Bangladesh and parts of Afghanistan. Called the Maurya empire, the capital was at Pataliputra.
Bumped west by the Huns (themselves "bumped" by the Chinese), a group of Turkic clans, called the Yueh Chi by the Chinese and the Tochari by the Romans, invaded Afghanistan and then north India, creating the powerful and mysterious Kushan kingdom around 50 AD. Kanishka, ruling around 100 AD, was the kingdom's most famous king, encouraging the spread of Buddhism. The kingdom was largely destroyed by Shapur I, shah of Persia.
South India was divided between the Kerala, Pandya and Cola kingdoms.