If we tell someone which book we have read or which movie we have seen and mention it for the first time,do we say
I`m reading a book 'Tom Soyer'.
I`m reading the book 'Tom Soyer'.
I have seen the movie 'The Da Vinci Code'.
I have seen a movie 'The Da Vinci Code'.
I understand that the indefinite articles are used when we mention something for the first time,but is the definite article possible in this case because we are talking about the book that is well-known? Should we use only 'a' and 'an' if the book,movie etc. is not well-known?
The rule is that a definite article ("the") is used to imply uniqueness, while an indefinite one implies the item is not unique. There is no difference for the "first" time.
"I am reading the book "Tom Sawyer" is correct.
If you replace "the" with "a" you remove the implication that the book is unique. If you use "the" where is seems out of context, such as "I ate the apple" there is an implication that the apple was in some manner unique, and that the listener should be able to understand why, that it makes a difference, and which apple you are talking about.