what dates marked the beginning and end of the Inca empire?

The Inca Empire included parts of modern day Peru, Chile, Argentina, and Bolivia.

The Incan dynasty began with the growth of Cuzco around 1200 AD; the Inca Empire began c.1438, after which it quickly expanded. It ended with the conquest of Peru by the Spanish between 1533 and 1542 AD.

For a full timeline, see related links below.