Ancient Greek was one of the best courses I had in university. It changed my view on language and western thinking quite a lot. My favorite words are

μαθηματικὴ (mathematike): If I remember correctly, it means 1. learning, 2. letter or book and 3. "everything there is to know (for certain)".

χαίρε (chaire): Used as a greeting, literally "be happy!"

Also it is funny that βαίνω (baino) means: I am walking, while "Bein" means leg in German - the amount of Ancient Greek words in German and other languages is ridiculously high.