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These 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., Comment: Some changes to the text, a diagram added

We associate to a braided 2-stack ${\cal C}$ a torsor, endowed with a symmetric cube structure (or $��$-structure), whose triviality is equivalent to the existence on ${\cal C}$ of a fully symmetric monoidal structure. In order to perform the analogous construction for braided 4-stacks, it is necessary to introduce the notion of a $��_3$-torsor pair, which is in the same relation to cubic forms as torsors with $��$-structure are to quadratic ones., 25 pages, Latex, xyPic