* As an adjective: You do not capitalize "Greek" when it's used as an adjective describing something, like "Greek mythology" or "Greek food."
* As a noun: You do capitalize "Greek" when it refers to a person from Greece or the Greek language, like "The Greeks are known for their history." or "I'm learning to speak Greek."
Here are some examples:
Not capitalized:
* He studied ancient Greek history.
* I love Greek yogurt.
* She is wearing a Greek dress.
Capitalized:
* The Greeks built amazing temples.
* I am learning the Greek alphabet.
* My friend is a Greek citizen.