N3
再び
ふたたび
Again, Once more, A second time
彼は刑務所から出て、再び犯罪を犯した。
After he left prison, he committed a crime once more.
Explanation
「再び」 is read 「ふたたび」 and means 'again'. Something that happened before and stopped comes back a second time (or more) after an interval. The tone is formal, used in news, history, papers and formal speeches: 「十年ぶりに再び優勝した」 (They won the title again after ten years); 「悲劇を再び繰り返してはならない」 (We must never repeat the tragedy).
Mixed up with
「もう一度」 is everyday speech, mostly a request or wish: 「もう一度言ってください」. 「また」 is very common in speech and writing, for repeated events ('here we go again'). 「再び」 is formal and written, for a major event happening once more.
Not for small daily requests: 「×再び言ってください」.
The reading 「ふたたび」 is often asked in vocabulary questions.