Structure of book chapters A few days ago I was approached to write a 10-20 page long chapter in a book in field of mathematics. I did a little research.  Authors are well known and no scam there. The issue is that this is my first experience and  would be great to know some of the charactristics of a book chapter in math ( research level).  How is it structured? Should one provide more background than typical academic papers?
I assume you were approached by one of the main authors, rather than an editor. They can answer your question as they know something about what they want the book to be. You might even be able to get a draft of another chapter if the project is in progress. But there is too much variability for a general answer here. Perhaps the background you would provide is already covered elsewhere in the book, for example. 

But it might also be that whatever you write as a first draft will need to be modified before it is accepted. You might have to do a lot of modifications so that the entire volume fits together properly.