The philologer and jurist William Jones was one of the first to see the relationship between Sanskrit, Greek, and Latin, as we can see in a lecture he gave to the Asiatic Society in Calcutta on 2nd February 1786, published two years later:
The Sanscrit language, whatever be its antiquity, is of a wonderful structure; more perfect than the Greek, more copious than the Latin, and more exquisitely refined than either, yet bearing to both of them a stronger affinity, both in the roots of verbs and the forms of grammar, than could possibly have been produced by accident; so strong indeed, that no philologer could examine them all three, without believing them to have sprung from some common source, which, perhaps, no longer exists; there is a similar reason, though not quite so forcible, for supposing that both the Gothic and the Celtic, though blended with a very different idiom, had the same origin with the Sanscrit; and the old Persian might be added to the same family.
Since then, researchers have discovered that this common language was supposedly spoken by a people living in southern Russia, north of the Caspian Sea. From there, they brought what Marija Gimbutas called the Kurgan culture into Old Europe, taking an Aryan culture to the East. This map shows the distribution of these Indo-European languages about 500 BCE.
In a natural evolutionary manner, they show a hierarchical structure, depicted here.