Could I use "the" after "there is/are"?
E.g.: There is the book on the table. There are the books on the table.
Or it must be: There is a book on the table. There are books on the table.
Could I use "the" after "there is/are"?
E.g.: There is the book on the table. There are the books on the table.
Or it must be: There is a book on the table. There are books on the table.
Yes, you can. You can use a definite article (the) before specified or particular nouns, whether they are countable or uncountable.
Specified or particular means, for example:
Definite, or previously mentioned ~ "I like the car you bought
Unique ~ "The Humber Estuary is not far away"
A natural phenomenon ~ "The rain is heavy"
A time period ~ "I lived there in the 1990s"
All the members of a society or a family ~ "The Smiths are coming for dinner"
So, if your books have been mentioned previously, you can say
"There are the books on the table".
If they haven't, maybe because you have just seen them, you would say
"Oh look! There are books on the table!"
You would not say "There is the book on the table".
You are using the definite article with the "There is/are" construction, and that is simply not done. You could, however, say "There is the book, on the table" or "There is the book - on the table", ie, adding additional, parenthetical information to the statement. And, of course, the indefinite article, among other things, is fine: "There is a book on the table", "There are some books on the table", etc.
Roaring Fish's sentences, while correct, are not examples of the "There is/are" construction.
See http://www.englisch-hilfen.de/en/grammar/there_is_there_are.htm