Cohomology with values in a sheaf of crossed groups over a site

This is an English translation of Raymond Debremaeker’s 1976 Dutch-language dissertation “Cohomologie met waarden in een gekruiste groepenschoof op een situs” (Katholieke Universiteit te Leuven). I thank the University librarians for sending me a copy of this text and Professor Debremaeker for allowing me to post this translation of his dissertation on this server. Work on this translation was supported by Chile’s Fondecyt through grants 1120003 and 1160004.