再……也…… / 再也不 / 没: however…, never again
【五55】【五57】紧缩复句、强调 / complex sentences
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
再 + adjective / verb + (subject) + 也 + verb means "however … it is, still …": a quick concession (这件事再难，我们也要坚持下去). 再也不 / 再也没 means "never again, no longer": 不 for a resolution or a future habit (我再也不去那家餐厅了), 没 for something that has not happened since a point in the past (他再也没给我打过电话).
Here 再 doesn't mean "again": it pushes the adjective to its limit ("however hard it is"). The pattern is shorter and more colloquial than 即使……也…… or 无论……都…… (HSK 3) and needs no conjunction: 再 + adjective is enough. A noun can open the sentence: 再小的问题，他也会认真地检查.
Don't mix it up with 再 "again" or with 又 (HSK 2): 再也不 looks forward (or at the present), "never again", whereas 又 reports a repetition that has already happened. The tone is lively speech, said angrily, resolutely or wearily.
Examples
我再也不去那家餐厅了。
Wǒ zài yě bú qù nà jiā cāntīng le.I'll never go to that restaurant again.
他走了以后，再也没给我打过电话。
Tā zǒu le yǐhòu, zài yě méi gěi wǒ dǎ guo diànhuà.Since he left, he has never phoned me again.
这件衣服再便宜，我也不会买。
Zhè jiàn yīfu zài piányi, wǒ yě bú huì mǎi.However cheap this garment is, I won't buy it.
雨下得再大，我也要去上班。
Yǔ xià de zài dà, wǒ yě yào qù shàngbān.However hard it rains, I'm going to work.
这件事再难，我们也要坚持下去。
Zhè jiàn shì zài nán, wǒmen yě yào jiānchí xiàqù.However hard this is, we must keep going.
再小的问题，他也会认真地检查。
Zài xiǎo de wèntí, tā yě huì rènzhēn de jiǎnchá.However small the problem, he checks it carefully.
Common mistakes
✗ 这件事难再也要做 → ✓ 这件事再难也要做 (再 goes before the adjective).
✗ 我决定再也没去那家店了 → ✓ 我决定再也不去那家店了 (没 is for the past, 不 for a decision).