TITLE: References for differential cohomology and differential characters
QUESTION [9 upvotes]: I am interested in learning differential cohomology and differential characters, and am currently studying these lecture notes on the subject. I sometimes feel it would be great if I could keep some more good references besides the lecture notes, as it could greatly help me speed up when I get stuck (which is happening often with me). Could someone please advise some alternate references which might supplement my study ?
I am familiar with elementary algebraic topology (singular homology & cohomology theories, basic homotopy theory) and differential geometry (connections, curvature, de-Rham cohomology, Chern-Weil theory).
Thanks ! 
Note : I earlier asked this question on m.se and offered a bounty but I did not get any answers there, I am taking the liberty of asking here.

REPLY [4 votes]: The following book has recently appeared:

Araminta Amabel, Arun Debray, Peter J. Haine (eds.), Differential Cohomology: Categories, Characteristic Classes, and Connections. Based on Fall 2019 talks at MIT's Juvitop seminar by: A. Amabel, D. Chua, A. Debray, S. Devalapurkar, D. Freed, P. Haine, M. Hopkins, G. Parker, C. Reid, and A. Zhang. (arXiv:2109.12250)