The wonderful book 'Descriptive Set Theory' by Kechris provides a rich theory on the Borel Hierachy (Chapter $22$). I am especially interested in the section $22$E 'The Difference Hierachy', which states that every set in the class $\Delta_{\xi+1}$ can be separated by transfinite difference of $\Pi_\xi.$
Question: Other than the above mentioned book, in what book can I look for to gain more information on difference hierachy?
I offer you to download this book: Kanamori "A The Higher Infinite Large Cardinals In Set Theory"
Also you can check: Early investigation of Borel degrees
The Wadge Hierarchy: Beyond Borel Sets