The correct word is (almost) always "rhetoric." It is a word meaning _the_ art of speaking or writing persuasively, so grammatically it is almost always singular. It is like "geometry" or "astronomy." It is (almost) always singular, never plural. It can also be an uncountable or mass noun, for a speaker's persuasive material. "His rhetoric was effective, and included effective use of jokes, contrasts, similes, metaphors, and a magnificent peroration." (Don't worry about what those all mean. All of these things were parts of the speaker's rhetoric). I suggest you stop reading here. However, as a technical detail: In theory, you could have more than one system of rhetoric. For example, if Aristotle had a slightly different kind of rhetoric from Cicero, one could say "Aristotle and Cicero's rhetorics were slightly different," just as one could talk of "the Greek and Arabic astronomies."

It s generally uncountable. So, it should be rhetoric o 's'.

The word is 'Rhetoric.' It never has an 's' according to the dictionaries I consulted. I have never heard it with an 's' Merriam Webster lists it with no 's' Correct: Rhetoric is a broad philosophy.... It is capitalized only at the beginning of a sentence.

It might be underlining it because you don't need need the s at the end, rhetoric should be fine on it's own. Because it's not a name or anything it doesn't need to be capitalised in the middle or end of a sentence. That's what I think anyway, might be best waiting for another answer to check I'm right.