再び means "again", "once more": something that had stopped happens a second time. It is an adverb and goes before the verb or at the head of the clause, and it belongs to writing, news and formal speech.
、。
The storm passed, and the sun came out once more.
。
We must make sure this problem doesn't happen again.
再び or また
is the everyday "again", in speech and writing alike. 再び is formal and a little weighty: a return after a gap, often after a change or an interruption. In conversation, use また.
、。
The war ended, and peace returned to the town once more.
In polite set phrases 再び fits, because the register is already formal.
。
It is an honour to meet you again.
二度と再び
with a negative is an emphatic "never again".
。
I will never do anything like this again.
。
I will never make a mistake like that again.
Lingaku