Some excerpt of comments in some questions

• Thanks a lot! Is there any chance you know of a reference where I could find the proofs of these facts? and the response is The standard reference is Giraud's book Cohomologie non-abelienne. This book is unreadable in the strongest possible meaning of the word "unreadable". So... no. Another users response is Depends on taste, André, 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. Response from another user is I don't think telling someone to see a dense 470 page book in French on non-abelian cohomology is a helpful comment.

Another excerpt from some notes by Breen and Messing is We now describe in more detail the content of the present text. While we have placed ourselves firmly within the context of algebraic geometry, in which the concepts of gerbes and stacks have been to date most fully developed.

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.

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