This is to announce a downloadable, slightly revised version of a 1988 preprint: Marco Grandis, Cohesive categories and manifolds, Dip. Mat. Univ. Genova, Preprint 76 (1988), published in 1990: –, Cohesive categories and manifolds, Ann. Mat. Pura Appl. 157 (1990), 199-244. The revised version of the preprint can be found at: http://www.dima.unige.it/~grandis/Chm.Pr1988(Rev.2013).pdf In the present version the text has been slightly modified, to make it less concise and clearer. Moreover, in the proof of the "cohesive completion theorem" (Section 9.2) a correction has been inserted, that was published in: –, Cohesive categories and manifolds - Errata Corrige, Ann. Mat. Pura Appl. 179 (2001), 471-472. With best regards Marco Grandis ________________________ The purpose of this article is to treat structures, like manifolds, fibre bundles and foliations, that can be obtained by glueing together 'elementary spaces' of a given kind. These structures are here defined by a sort of glueing atlas, and - formally - as symmetric enriched categories over suitable 2-categories. Their morphisms are defined as 'compatible profunctors'. The basis of the enrichment, called 'cohesive' and 'e-cohesive categories', are equipped with an order and a compatibility relation; they extend inverse categories and the categories of partial mappings. Two completion theorems, with respect to compatible joins and the glueing of 'manifolds', play a crucial role. This matter was presented at the meeting 'Categorical Topology', Prague 1988 (see [G4]) and is developed in the present work. Applications to partially defined operators between Banach spaces were given in [G5], also published in 1990. The links of this setting with Ehresmann's pseudogroups [E1, E2] and Lawvere's view of mathematical structures as enriched categories [La] are examined in the Introduction. Dominical categories and p- categories, that are also related with partial mappings and were previously introduced in the 1980's by Heller, Di Paola and Rosolini [He, Di, DH, Ro], have a natural e-cohesive structure (see Section 3.8). Later, e-cohesive categories have also been used under the name of 'restriction categories' and equivalent axioms. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]