The Greek language (Ελληνικά) is one of the Indo-European languages, brought to Greece by the Achaeans around 1700 BC. Originally there were a variety of spoken dialects, most notably Ionic, Doric, and Attic.
Attic Greek was the language of Athens; most of the surviving classical Greek literature is in Attic Greek. Alexander the Great, besides being a great military leader, was instrumental in combining these dialects to form Koine Greek (from the Greek word for "common") (sometimes called New Testament Greek after its most famous work of literature). This allowed his combined army to communicate and was also taught to the inhabitants of the regions that he conquered, turning it into a "world language". The language evolved during the Hellenistic period, and for many centuries was the "Lingua Franca" of the Roman Empire. From this descended the Greek that was the official language of the Eastern Roman Empire (or Byzantine Empire) and finally the modern Greek of today.
Greek, like many other Indo-European languages, is highly inflected -- for example, nouns have 5 cases, 3 genders, and 3 numbers, verbs have 3 moods, 3 voices, as well as 3 persons and 3 numbers and various other forms. Here is the definite article declined:
|Dative (indirect object+)||tô||tê||tô||tois||tais||tois|
|Accusative (direct object)||ton||tên||to||tous||tas||ta|
Modern Greek has lost the dative (except in a few expressions like en taxei OK), but the other forms are not much changed:
Have a look at the Greeklish article.