Many - it means "a lot of" with countable nouns.
These are some of the many questions to which we have no answer.
Several - it means "a couple of", "some", "a few", you can use it for example in that way:
I was ill for several days. (It was only few days, not many of them.)
Multiple - as an adjective it means, that you have for example more, than one option to choose:
"They can ask in multiple ways, but the most common are the following."
You can also use it to show plural number of something.
"Many of these women have multiple children with various men."
This word is connected with numbers too, because you can say:
"The number 18,980 is the least common multiple of 260 and 365" and now it is a noun.
You can also find many other uses of these three words and find several examples.