a lot of=lots of,很多的,没有a lots of的说法.
few表示否定,几乎没有,后面接可数名词,比如there are few people in the room.房间里没人.
a few,表示几个.
他们和little/a little对应,只是这两个词后面接不可数名词,比如little water.
a number of=many,表示很多
the number of表示···的数量是,比如the number of the students is 56.学生的数量是56.