The English language, and indeed most European languages, traces it original roots back to a Neolithic (late Stone Age) people known as the Indo-Europeans or Proto-Indo-Europeans, who lived in Eastern Europe and Central Asia from some time after 5000 BC (different hypotheses suggest various different dates anywhere between the 7th and the 3rd millennium BC)
The exact nature of the original Indo-European language was not known as no writings exist from that time (the very earliest examples of writing can be traced to Sumeria in around 3000 BC), so knowledge of it is necessarily based on conjecture, hypothesis and reconstruction. Using the “comparative method”, though, modern linguists have been able to partially reconstruct the original language from common elements in its daughter languages.
Indo-European is just one of the language families, or proto-languages, from which the world's modern languages are descended, and there are many other families including Sino-Tibetan, North Caucasian, Afro-Asiatic, Altaic, Niger-Congo, Dravidian, Uralic, Amerindian, etc. However, it is by far the largest family, accounting for the languages of almost half of the modern world’s population, including those of most of Europe, North and South America, Australasia, the Iranian plateau and much of South Asia. Within Europe, only Basque, Finnish, Estonian, Hungarian, Turkish, and a few of the smaller Russian languages are not descended from the Indo-European family.
Sometime between 3500 BC and 2500 BC, the Indo-Europeans began to fan out across Europe and Asia, in search of new pastures and hunting grounds, and their languages developed - and diverged - in isolation. By around 1000 BC, the original Indo-European language had split into a dozen or more major language groups or families, the main groups being:
Hellenic
Italic
Indo-Iranian
Celtic
Germanic Armenian
Balto-Slavic
Albanian
These broad language groups in turn divided