Final answer:
The process by which Greek culture spread throughout the Near East following Alexander the Great's death is known as the Hellenistic era. It was marked by the establishment of Greek-style cities and a blending of Greek and local cultures across the Middle East and as far east as India.
Step-by-step explanation:
Following the death of Alexander the Great in 323 B.C., the Near East was influenced by Greek culture in a process we call Hellenistic. The period known as the Hellenistic era saw Greek civilization, culture, and ideas spread across the entire Middle East as far as modern India. In this time, Greek cities were founded, complete with institutions such as temples, theaters, agoras, and gymnasia, to emulate the homeland for Greek and Macedonian colonists. This era also experienced a blending of cultures, with artistic expressions reflecting a mix of motion, emotion, and classical styles. This period of cultural diffusion was both initiated and catalyzed by Alexander's conquests and continued under the rule of his generals, who established new dynasties and traded significantly with neighboring regions, including India.