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These notes are slightly edited notes of a mini-course of 4 lectures delivered at the Vietnam Institute for Advanced Study in Mathematics in August 2013. The aim of the course was to introduce participants to joint work of the author with Goerss, Karamanov, Mahowald and Rezk which uses group cohomology in a crucial way to give a new approach to previous work by Miller et al. (Ann. Math. 106:469–516, 1977), and by Shimomura and his collaborators (Shimomura, J. Math. Soc. Jpn. 52(1):65–90, 2000; Shimomura, Topology 41(6):1183–1198, 2002; Shimomura and Yabe, Topology 34(2):261–289, 1995). This new approach has lead to a better understanding of old results as well as to substantial new results.

A Mini-Course on Morava Stabilizer Groups and Their Cohomology