Giraud develops a theory of nonabelian cohomology in a very general setting. His $H^2$ classifies the gerbes bound by a given band (lien). It is written in the style of EGA, which many of us find unattractive. There is a 4 page summary in the appendix to Tannakian Categories by Deligne and Milne. jmilne.org/math/xnotes/tc.html