2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121821These notes discuss in an informal manner the construction and some properties of 1- and 2-gerbes. They are mainly based on the author's previous work in this area, which is reviewed here, and to some extent improved upon. The main emphasis is on the description of the explicit manner in which one associates an appropriately defined non-abelian cocycle to a given 1- or 2-gerbe with chosen local trivializations.Some changes to the text, a diagram addedCategory TheoryHigh Energy Physics - TheoryAlgebraic GeometryAlgebraic Topology18D05; 14A20; 55R70text