This thesis was available as part of Esquisses Mathematiques 32 (1983). Andree Ehresmann kindly supplied an example of this issue, and Stephen Gaito recently scanned it so that it is now available from http://ehres.pagesperso-orange.fr/Cahiers/dakinEM.pdf This thesis defines the notion of simplicial T-complex, a simplicial set with in each dimension > 0 a set of elements called `thin' satisfying the conditions T1) Degenerate elements are thin; T2) every horn has a unique thin filler; T3) if all faces but one of a thin element are thin, then so is the remaining face. It develops some of the relations with groupoids, crossed modules and crossed complexes. Other parts of this issue of Esquisse will be made available in due course. Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]