Indo-Iranian Branch:
* Indo-Aryan: Hindi, Urdu, Bengali, Marathi, Punjabi, Gujarati, Nepali, Sinhala, Romani, etc.
* Iranian: Persian, Kurdish, Pashto, Tajik, Ossetian, etc.
Italic Branch:
* Romance Languages: Spanish, Portuguese, French, Italian, Romanian, Catalan, etc.
* Extinct Languages: Latin, Oscan, Umbrian, etc.
Germanic Branch:
* West Germanic: English, German, Dutch, Afrikaans, Yiddish, etc.
* North Germanic: Swedish, Norwegian, Danish, Icelandic, Faroese, etc.
* East Germanic: Extinct languages like Gothic.
Balto-Slavic Branch:
* Baltic: Lithuanian, Latvian.
* Slavic: Russian, Ukrainian, Polish, Czech, Slovak, Bulgarian, Serbian, Croatian, Slovene, etc.
Celtic Branch:
* Insular Celtic: Irish, Scottish Gaelic, Manx, Welsh, Cornish, Breton.
* Continental Celtic: Extinct languages like Gaulish.
Greek Branch:
* Ancient Greek: (extinct)
* Modern Greek: Spoken in Greece and Cyprus.
Armenian Branch:
* Armenian: Spoken in Armenia and diaspora communities.
Tocharian Branch:
* Tocharian A and B: Extinct languages spoken in the Tarim Basin in Central Asia.
Anatolian Branch:
* Hittite: Extinct language spoken in Anatolia.
* Luwian: Extinct language spoken in Anatolia.
* Other Anatolian languages: Extinct languages like Lydian, Lycian, and Palaic.
This is not an exhaustive list, as there are many other languages and dialects within these branches, and some languages have uncertain classifications. Additionally, the relationships between some branches, like the Tocharians, are still being researched.