再（ふたた）び is a 副詞（ふくし） (adverb) that means ‘to repeat’. It is regularly translated as ‘again’, ‘once more’, or ‘a second time’. Usually,
再（ふたた）び will appear at the beginning of a sentence, before some sort of request or statement will be made about what needs to be repeated.
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彼（かれ）は刑務所（けいむしょ）から出（で）て、再（ふたた）び犯罪（はんざい）を犯（おか）した。
After he left prison, he committed a crime once more.
再（ふたた）びふるさとに戻（もど）りたいです。
I want to go back to my home town again.
Despite meaning ‘to repeat’,
再（ふたた）び specifically has the nuance of repeating something ‘for the second time’. Because of this, it will not be used to highlight things that need to be repeated over and over again.
Unlike また, which is frequently used to express ‘again’,
再（ふたた）び is quite formal, and will be seen far more often in books/articles, than it will be spoken.
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また来週（らいしゅう）会（あ）いましょう。 (Natural)
Let's meet again next week.
再（ふたた）び来週（らいしゅう）会（あ）いましょう。 (Unnatural)
Let’s meet once more next week.