I am looking for some references related to gerbes and their differential geometry. Almost every article I have seen that is related to gerbes there is a common reference that is Giraud's book Cohomologie non-abelienne. For me, it is not readable as I can not read french.


Only references I am familiar with are


* <https://arxiv.org/abs/math/0212266> Introduction to the language of stacks and gerbes
* <https://arxiv.org/abs/math/0106083> Differential Geometry of Gerbes
* <https://arxiv.org/abs/math/0611317> Notes on 1- and 2-gerbes


Out of these, only first article is more or less readable. The other two by Lawrence Breen are really not readable for me. 


Some excerpt of comments answering such a request were


* "The standard reference is Giraud's book Cohomologie non-abelienne. This book is unreadable in the strongest possible meaning of the word *unreadable*."
* "I find most of the contemporary articles in this area, which are often nonsystematic in terminology and notation, plus wave hands and use jargon on most issues, much less readable than Giraud's book."
* "See Giraud's book on nonabelian cohomology."
* "I don't think telling someone to see a dense 470 page book in French on non-abelian cohomology is a helpful comment."


I am getting demotivated and irritated by lack of notes on gerbes and even in Mathoverflow there are not so much to see. Is this out of fashion now? Are there any one else who read/work on these? Iam not looking for something in Physics perspective.



References on Gerbes
The book of Giraud is a fundamental reference on the subject, but you have to be used to the language of Grothendieck. A reference more accessible, for example for a differential geometer is the chapter 5 of the book of Brylinski which deals only with commutative gerbes.


J.L Brylinski Loop Spaces, Characteristic Classes and Geometric Quantization.


