Since the 1500s European visitors to India noticed the similarities between most European and many Indian languages. In 1786 the scholar and jurist Sir William Jones, in a lecture at the Asiatic Society of Bengal in Calcutta, first proposed that many of the oldest languages in both Europe and Asia, including Greek, Latin, Persian, and Sanskrit, were so similar that they must have stemmed from a common source. The word "Indo-European" was later developed to describe what was seen as a family of languages, going back to a single "proto-Indo-European language" spoken in central Asia some 5-6,000 years ago.
Over the past century linguists have tried with some success to classify all the world's languages into a number of 'families'. Some have even proposed combining these into 'super families' or even the idea of a single original language from which all super-families originate.
This image is a tree of the world's major language families drawn up by Ma Pinky Htut Aung at U Thant House. The number next to each language represents the approximate number of people (in millions) who speak the language today.
As you will see, the biggest tree is the "Indo-European" one which includes nearly all Europe's languages as well as the languages of the northern part of the Indian subcontinent. English is part of the Germanic branch. Hindi and Bengali are part of the Indo-Aryan branch.
The languages spoken in Myanmar are usually classed as Tai-Kadai, Tibeto-Burman, or Austro-Asiatic. Shan is an example of a Tai-Kadai language. Burmese (Myanmar), Jingpaw and Lisu are all Tibeto-Burman. Tibeto-Burman languages in return are related to Mandarin and other languages in China. Mon, Wa and Palaung are Austro-Asiatic languages related to Vietnamese and Khmer. Also, Indo-European languages (Sanskrit, Pali, and later English) have been languages used in Myanmar since writing in Myanmar first began nearly two thousand years ago.
It should be noted that there are no universally accepted classifications and many different ways language trees can be drawn. Some will also challenge the very idea of a 'tree' as a way to think about language connections. Languages are of course always changing and most of the languages spoken today are very different from their ancestors just a few hundred years ago.
It should also be noted that these are all linguistic connections, which may or may not be linked to any genetic connections. In America most people speak English, but that doesn't mean their genetic ancestry goes back to people in England a thousand years ago or that they are related genetically to other speakers of Germanic languages. They may instead be descended from people from Italy, Russia, Africa or Japan.
In the same way, the languages people speak in Myanmar and the relationship between these languages may not tell us much about other aspects of the country's history. That Mon is similar to Vietnamese and Burmese is not, for example, may say very little about the historical connections between communities currently speaking these languages.