It is fairly well known that strict 2-groups, that is to say strict 2-categories in which there is a single 0-cell and all one cells are invertible, are equivalent to crossed modules. Geometric realizations of strict 2-groups realize all homotopy 2-types. Strict n-groups do not realize all homotopy n-types, but rather only "twisted generalized Eilenberg-Mac Lane spectra." Loday proved that n-fold categories in groups represent all homotopy n-types. The search for the right approach to weak n-groupoids is in part a search for a model for homotopy n-types in which the k-fold loop spaces sit nicely. We will examine some of these ideas starting from the beginning--the definition of strict n-category--and proceeding not much past what the speaker has managed to learn so far.