たとえ, coming from 例（たと）える, a る - Verb meaning ‘to speak figuratively’, is a word in Japanese that is often used with ても (or でも), in order to present possibilities. たとえ is primarily seen at the beginning of a sentence, before some kind of possibility, comparison, or supposition will be stated.

• 空手（からて）ではたとえ試合（しあい）で勝（か）っても、ガッツポーズをしてはいけない。
  Even if you win in a karate competition, you should not celebrate visibly.
• たとえ暑（あつ）くても、虫（むし）が入（はい）ってくるのでこの窓（まど）は開（あ）けないで下（くだ）さい。
  Even if it is hot, bugs will come in, so please do not open this window.
• たとえ好（す）きでも、そんなことをされたら、嫌（きら）いになる。
  Even if I like them, if someone says such a thing, I will start to dislike them.
• たとえ電車（でんしゃ）でも30分（ぷん）はかかる。
  Even by train, it will take at least 30 minutes.

たとえ tends to be used to present situations where ‘even if they were true, (B) still may/may not happen’. This is called a ‘contrastive’ example. もし on the other hand tends to be used for examples in which (A) will directly result in (B). This is called a ‘resultative’ example.

• たとえ来年（らいねん）までに完成（かんせい）したとしても、中（なか）に入（はい）る店（みせ）が決（き）まっていないから来年（らいねん）中（じゅう）にはオープンされないだろう。
  Even if it is completed by next year, the shops that it is going in have not been decided, so it is unlikely that they will open next year.
• もし今年（ことし）中（じゅう）にモールの工事（こうじ）が終（お）わったら、来年（らいねん）の頭（あたま）にはオープンするはず。
  If the construction for the mall finishes within this year, it should open at the beginning of next year.