German is a Western Germanic language, and evolved from the same language as English, Dutch, Yiddish, and a few other minor languages. West Germanic, as its name implies, is part of Germanic, which also includes Scandanavian (Swedish, etc.), and East Germanic (Gothic and a few other dead languages of sackers of Rome).
Germanic, in turn, is part of Indo-European, along with Balto-Slavic (such Lithuanian and Russian), Celtic (such as Irish), Italic (which includes the Romance languages like French and Spanish), Greek, Albanian, Indo-Iranian (which includes most of the languages of Iran, Pakistan, and northern India, and also the language of the Gypsies), and Armenian. Indo-European, along with several dead languages of Anotolia (modern-day Turkey), including Hittite, is part of a family called Indo-Hittite. Indo-Hittite and Indo-European are essentially the same, but the Anatolian languages seem not to be very different from the rest of Indo-European, so the the name Indo-Hittite is used to reflect that.
Indo-Hittite, in turn, may be part of a still larger family, called Eurasiatic (or sometimes called Nostratic). Eurasiatic also includes the families Uralic-Yukaghir (which includes Hungarian, Lapp, and Finnish), Altaic (which includes Turkish and Mongolian), Japanese and Korean (which are part of one family), Eskimo-Aleut, and a few other languages of Siberia.
I have a more detailed lineage of Eurasiatic, as well as for Indo-European/Hittite.
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