Greek culture significantly influenced Western Europe through the spread of Hellenistic ideas, art, philosophy, and political thought, particularly after the conquests of Alexander the great. The Roman Empire adopted and adapted Greek culture, which included literature, architecture, and governance, helping to disseminate these ideas across Europe. The Renaissance further revived Greek philosophy and aesthetics, leading to a profound impact on European art, science, and intellectual life. As a result, many foundational concepts of Western civilization, including democracy and rationalism, can be traced back to ancient Greek culture.
First the Greek, later the Roman culture.
Greek mythology has had influence on the culture, the arts, the literature and remains part of Western heritage and language.
Through the Renaissance.
The three ancient civilisations that most profoundly influenced modern Western culture would probably be Rome, which gave us its empire; Greece, which gave us its philosophy and ideals; and Judea, which gave us Christianity.
The fall of the western part of the Roman Empire was a factor in the decline in the influence of Greek culture in western Europe. The Romans were deeply Hellenised (influenced by the Greeks). Their art became Greco-Roman and they adopted Greek medicine and two schools of Greek philosophy. After the fall of the western part of the empire Christian western Europeans begun to look on the Romans as pagans and rejected Roman culture and through this knowledge of Greek culture also disappeared. This did only apply to the eastern part of the Roman Empire. It was not affected by the invasions by the Germanic peoples which led to the fall of the west and continued to exist for nearly 1,000 years. Historians use the term Byzantine Empire to indicate the eastern part after the fall of the western part. The people in question did not know this term and called their empire Roman Empire. After the fall of the west, this part of the empire became Greek in character. It preserved ancient Greek learning. When Constantinople (the Byzantine capital) fell to the Turks in the 15th century, Byzantine scholars fled to Italy and reintroduced ancient Greek learning in western Europe.
The influence of the greek culture faded , after Alexanders kingdom was divided into three areas, and later on the roman culture also made its way.
The Renaissance was the period in history most influence by classic Greek and Roman works. After the fall of Constantinople, many Greek and Roman scholars fled to Italy and Western Europe, prompting a new surge of interest in ancient literature and a desire to reproduce their culture.
Western Europe is far more developed, less corruptable (though this is not to say Eastern Europe is corruptable, just less than Western Europe), and less powerful (economically wise and most likely military wise as well). Western Europe has also been more involved in foreign affairs in the global world.
The Romans.
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Greek
The influence of Greek culture faded when the Roman Empire rose to power in the Mediterranean. Romans adopted and adapted many aspects of Greek culture, but over time developed their own unique identity that eventually diluted the impact of Greek cultural influence.