There are many places where you can organize a reading nook or any other personal reading space. One of them is to use this dead space under stairs.
To do that you need to think through some things. First of all there should be a comfortable seating solution. Several bookshelves would be also nice to organize your current books. The last but not least thing to consider is light. You definitely should put a good lamp there because most likely there won’t be enough natural light.