We use amount of with uncountable nouns. Number of is used with countable nouns:

We use a huge amount of paper in the office every day.

The amount of time it took to finish the job was very frustrating.

A great number of students volunteer each year for environmental projects.

Not: A great amount of students volunteer …

I have a number of things I want to talk to you about.

Quantity is more formal than amount or number. A quantity of or quantities of can be followed by a countable noun or an uncountable noun. They are most commonly used with an adjective such as huge, big, large, small:

The soldiers discovered a large quantity of weapons hidden under the floor of a disused building. (countable)

You only need a very small quantity of cement to mix with the sand. (uncountable)

Large quantities of illegal drugs had been discovered. (countable)

Aid workers have delivered huge quantities of food to the refugee camps. (uncountable)