また + [verb] [sentence]。また、[sentence] [noun] + もまた + [predicate] またの + [noun]
また means "again": something that happened before happens once more. It is an adverb and goes before the verb, or at the front of the sentence.
When the thing that repeats is unwelcome, また carries the speaker's irritation.
Both can be "again", but もういちど一度 is "one more time, now", and it is what you say when you ask someone to repeat something. また points at some later occasion.
At the start of a sentence, followed by a comma, また adds a further point: "also", "moreover". This is the register of writing and presentations. In conversation, それに or あと is more usual.
These go beyond "again" and "also".
After a noun with も, また adds weight to the "too": this one is no exception. It is a little formal.
Before a noun, また gives "another", "yet another". またの appears in set phrases such as またのきかい機会 (another occasion).