The phrases amount of and number of have slightly different meanings.

Amount of is used with uncountable singular nouns. Uncountable nouns are those nouns that refer to things you cannot measure or count. Examples are: hate, beauty, respect, information etc.

• A computer can store a vast amount of information.

The noun information is both singular and uncountable – it refers to an idea that cannot be measured.

• Almost all of us have to deal with a certain amount of stress.

The word stress refers to an idea that cannot be measured.

• A certain amount of confidence is absolutely essential for success in life.

The nouns amount and number are both used to talk about quantities. Amount is used before uncountable nouns. Number is used before plural nouns.

Compare:

• That website receives only a small amount of traffic. (Traffic is an uncountable singular noun and hence we use amount of.)
• That website receives only a small number of visitors. (Visitors is a plural noun and hence we use number of.)

The words amount and number can be modified by the expressions small and large. Note that big and little are not normally used with amount and number.

• A large number of people want to buy cars. (NOT A big number of people want to buy cars.)
• You only need to contribute a small amount. (NOT You only need to contribute a little amount.)