Which areas on the map did alexander the great conquer?

Persia 

Alexander the Great of Macedonia, possibly regarded as the greatest ever military commander, led his army from Greece through Turkey to what is now Iran, Persia, through to what is now Pakistan, parts of India & Afghanistan . . . . . Notable victories include Guatamela, the Hydaspes, the Granicus & Issue's. 
Egypt, Persia, Asia Minor, Syria, & what is now parts of Pakistan, India & Afghanistan.

He conquered Greece, Egypt, Persia, and part of the Indus Valley in India and named many cities after himself, like Alexandria in Egypt which became a center of commerce for Hellenistic culture.
Egypt, the Middle East and central Asia.