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Much, many, a lot
We use much with singular uncountable nouns and many with plural nouns.
e.g There is much rain (in December).
e.g. There is many sandals.
A lot of (and lots of) can be use in both countable and uncountable nouns.
e.g There is a lot of rain (in December).
e.g. There is a lot of sandals.
Quantity adverbs
Countable nouns are things which can be counted. That means that when there is more than one of them, you need to add 's'. Also, when a countable noun is singular an article (a/an/the) is often used with it.
e.g. There are too many gladiators in the Coliseum.
Non-Countable Nouns are usually things which cannot be counted, such as rice or water. Non-countable nouns only have a singular form, but we either use the word "some" or nothing at all instead of an article.
e.g. There is too much smoke.