The indefinite article part 2

The indefinite article can be used to refer to:
-categories (one element represents the whole class or gender)
A cat is an animal.
An American is a person who lives in America.
An employee has to respect his superior.

-a person,objet, idea etc that is introduced in the conversation for the first time:

Ana: A woman stopped me yesterday in the street.(Ana introduces the unknown element in the conversation)
Betty: Did you know the woman? (Betty asks a question by saying 'the woman' because the element 'woman'was already introduced in the conversation)

And what if the woman was familiar to both speakers?

Ana: The woman you introduced me yesterday stopped me in the street.
Betty: What did the woman say?

In this case Ana starts the conversation by saying 'the woman you introduced me'-which means a particular woman, one which is known by both of them.

The difference between 'a' and 'one'.

Many people do not know when to use 'a' and when to use 'one'.
a book- means 'any book', it does not point to any in particular
one book- since 'one' is a cardinal numeral , it refers to the quantity of objects:

I want one book, I don't need two books.