〜ても
Even if… (concession)machine translation
Formationて-form + も (verbs: 行っても; い-adjectives: 高くても; nouns and な-adjectives: 雨でも・暇でも)
ても is the CONTRARY conditional: "even if A, B still happens." While たら・ば・と say "if A, then B follows," ても says the opposite — B happens regardless of A. Forming it is very familiar: take the て-form and add も. い-adjectives become くても (高くても); nouns and な-adjectives use でも (雨でも、暇でも).
Clause A can be a hypothetical that hasn't happened (雨が降っても行きます — even if it rains, I'll still go) or a general truth (いくら高くても — no matter how expensive). Compare this pair of sentences to see ても's role clearly: 雨が降ったら、行きません (if it rains, I won't go) ↔ 雨が降っても、行きます (even if it rains, I'll still go). Just swapping たら for ても flips the whole direction of the sentence.
Don't confuse it with two old acquaintances: 〜てもいい (permission to do something — which you learned at N5) is just ても plus いい turned into an asking-permission pattern, and のに also translates as "and yet" but is only used for things that HAVE actually happened, carrying a sense of surprise or regret. ても is broader: use it freely for both hypotheticals and facts, and the second clause is unrestricted — commands and expressions of intent are both fine.
Examples
雨が降っても、試合があります。
Even if it rains, the match will take place.
高くても、この辞書を買います。
Even if it's expensive, I'll buy this dictionary.
日曜日でも、父は仕事に行きます。
Even on Sundays, my father goes to work.