This is to announce the posting at the los alamos site of the following paper: to download the paper: http://arXiv.org/abs/math.CT/0208222 Title: On the representation theory of Galois and Atomic Topoi Authors: Eduardo J. Dubuc Comments: 34 pages Subj-class: Category Theory We elaborate on the representation theorems of topoi as topoi of discrete actions of various kinds of localic groups and groupoids. We introduce the concept of "proessential point" and use it to give a new characterization of pointed Galois topoi. We comment and develop on Grothendieck's galois theory and its generalization by Joyal-Tierney, and related work on these theories within the contex of topos theory by other authors. We have the hierarchy (for connected topoi): 1. essentially pointed Atomic = locally simply connected. 2. proessentially pointed Atomic = pointed Galois. 3. pointed Atomic The corresponding group of automorphisms of the point in the fundamental theorem are: 1. discrete group. 2. prodiscrete localic group. 3. localic group. We analyze also the respective groupoid versions (allways for connected topoi) and show that the groupoid in the fundamental theorem can allways be interpreted as the groupoid of all points. 1. connected discrete groupoid. 2. connected groupoid with discrete space of objects and prodiscrete localic spaces of hom-sets. 3. connected groupoid with discrete space of objects and localic spaces of hom-sets. We analyze also the unpoited version, and show that for a Galois topos, may be pointless, the groupoid can also be considered as the groupoid of "points". 1. allways with points. 2. connected (may be pointless) prodiscrete localic groupoids. 3. we do not know how to define the groupoid of points for a unpointed (may be pointless) connected atomic topos. 30-Sep-2002 14:23:08 -0300,869;000000000000-00000000