The first systematic theory of the relationships between human languages began when Sir William Jones proposed in 1788 that Greek and Latin, the classical languages of Europe, and Sanskrit, the classical language of India, had all descended from a common source. The evidence for this came from both the structure of the languages -- Sanskrit grammar has similarities to Greek and to nothing else -- and the vobcabulary of the languages. Thus, "father" in English compares to "Vater" in German, "pater" in Latin, "patêr" in Greek, "pitr." in Sanskrit, "pedar" in Persian, etc. On the other hand, "father" in Arabic is "ab," which hardly seems like any of the others. This became the theory of Indo-European languages, and today the hypothetical language that would be the common source for all Indo-European languages is called Proto-Indo-European.
(http://www.departments.bucknell.edu/linguistics/lectures/05lect22.html)

The ancient hieratic language of India is called Sanskrit, actually sam-skrta or "decorated, arranged language", and dates from the end of the second millennium B.C. A vast body of religious materials was assembled, the best known and earliest is the Rg Veda which we have entire in a long MS tradition but also reinforced by a remarkably accurate oral tradition passed down through the ages. Sanskrit as we have it is a literary language, high decorated and furnished with a body of linguistic and grammatical interpretation dating from ancient times. For practical instruction purposes, Sanskrit it even today for a small body of special students the Indic parallel to Latin studies in the West. It belongs to the group of Indo-European (IE) languages which came down along with Iranian from the north, to invade the Indic sub-peninsula, and was carried by the ksatriya class of northern warriors who dominated India for centuries.

These warlike peoples, whatever their actual ethnic composition, called themselves Aryah or Aryans and their language represents an early offshoot from the IE outpouring from the area south and east of present Russia. Note that when we speak of language groups, we are speaking in wholly linguistic terms, and must not confuse language-groups with ethnic entities.

If Indo-Iranian groups represent an early IE offshoot, we should note that the Hittites of Eastern Anatolia represent as early a spur from the westward linguistic flow. It was only in the early years of the 20th century that clay tablet written in cuneiform characters were discovered near the Turkish village of Boghaz-koi, but it was some twenty years before they were deciphered and understood as a very early and rather surprising variety of IE derivation. The Hittite Empire was a major contender for power in the 2/1 millennium B.C., but nobody thought that their language was a form of the IE stock. Some even felt that Hittite may have been the parent of the IE languages, hence on the same level with IE itself, a view proposed and studied for years by Sturtevant of Yale. But it is now felt that Hittite is simply an IE cousin, although it shows remarkable deviancy from what we consider the norm of early IE structure.

Greek was early carried down from the north into the Greek peninsula, again in early 20th c. major discoveries of "Linear" tablets written on clay were found at various sites on Crete and southern Greece. In l949 the English cryptanalyst Ventris cracked one portion of this tablet treasure-trove and proved that it was an early form of Greek, dating well back into the times of an unknown empire in the second millennium B.C. The writing indicates large commercial ventures, shipping and production of many basic items of trade. We call these translatable documents Linear B, but the Linear A has so far resisted interpretation and may belong to a lost language stock of which we have no other traces.

After 1200 B.C. a general period of desiccation seems to have curtailed this early civilization's life, and it was only after 800 B.C. that our history of ancient Greece starts up again, apparently largely anew with only folklore information about the ancient days at Troy and Cnossos. The later Greek language in the historical period divides itself into several dialects which are largely mutually intelligible, but these are in turn replaced by the politically dominant Athens with Attic Greek, the language of the culture from then on.
http://community.middlebury.edu/~harris/LatinBackground/IndoEuroBackground.html
(Compiled from several scholars posting on various sites on the web.)