たとえ〜ても
even if
たとえ + て-form + も · たとえ + Noun + でも
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たとえ at the start of a clause signals that a ても ("even if") is coming: たとえ雨が降っても、試合は行われる, "even if it rains, the match will go ahead".
It adds emphasis and a sense of determination: whatever happens, the result won't change. たとえ失敗しても、後悔しない, "even if I fail, I won't regret it".
After a noun, the pair is たとえ〜でも: たとえ冗談でも, "even as a joke". It also pairs with としても: たとえ反対されたとしても.
It's the ても version of もし: もし goes with たら and ば ("if"), and たとえ goes with ても ("even if"). Mixing them (たとえ〜たら) is a common slip.
Examples
たとえ雨が降っても、試合は行われる。
Even if it rains, the match will go ahead.
たとえ反対されても、私は行く。
Even if people are against it, I'm going.
たとえ失敗しても、後悔しない。
Even if I fail, I won't regret it.
たとえ冗談でも、そんなことは言わないで。
Even as a joke, please don't say things like that.
たとえ時間がかかっても、最後までやります。
Even if it takes time, I'll see it through.