A Greek is a person descending from the residents of Greece; the Greek term for a Greek is a Hellene, as they call their land Hellas. In period, "Greek" was used to describe Byzantines, who referred to themselves as Byzantine or Roman.
There are several distinct varieties of the Greek language throughout history, starting with the Attic Greek of the classical Hellenic period, the Koine of the Hellenistic and Roman eras and during period Byzantine Greek, spoken throughout Greece and Byzantium.
Much the classical scientific and medical literature was written in ancient Greek. We can thank the Arabs for translating the documents into Arabic which was then retranslated into Western European languages during and following the Crusades, especially those involving the Spanish Moors.