In all the japanese learning books, they teach you that xxxday ends with 曜日.
But sometimes I get to see xxx曜 only without the "Day" Kanji.
Can I shorten it when speaking too or is it only written ? And when can I shorten it ?
It is not clear cut, but my impression is that the tendency is that 日曜日 means a particular day that is Sunday whereas 日曜 means Sunday in general or series of Sundays.
When it is clear that it is not about a particular day but is about a series of days, this contrast becomes clear.
When you say
do you mean in your books? Or other places too?
I personally only use it in informal situations like speaking with/emailing friends. I can't say I've ever seen it written this way non-informally.