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We use much with singular uncountable nouns and many with plural nouns:

[talking about money]

I haven’t got much change. I’ve only got a ten euro note.
Are there many campsites near you?

Much and many are also more formal than a lot of.

Much and many are used in negative sentences, whereas a lot of is used in positive sentences.

I don’t have much money, but I have a lot of good friends.

Lots of functions similarly to a lot of, but is more informal.

From the Cambridge Dictionary. Click on the link to learn more.