This is the kickoff of a series of talks aimed at understanding the recent work of Gukov, Kapustin and Thorngren on higher gauge theory and gapped phases in TQFT. I will start with a review on the definition of a U(1)-gerbe and then generalize it to nonabelian gerbe, with the U(1)-group replaced by a (strict) Lie 2-group. I will also discuss connections on nonabelian gerbes and their surface holonomy.