A recent discussion on the category list has been continued on http://mathoverflow.net/questions/199849/brandts-definition-of-groupoids-192... While trying to confirm my recollections of the interest of Reidemeister in groupoids I did a web search on Reidemeister 1932 Topologie, and to my pleasure saw on arxiv:1402.3906 Translation of Reidemeister's "Einf??hrung in die kombinatorische Topologie" John Stillwell <http://arxiv.org/find/math/1/au:+Stillwell_J/0/1/0/all/0/1> I am writing to advertise this translation. Reidemeister has a section on "The groupoid", defines the fundamental groupoid, and also the action groupoid corresponding to a group action. I believe the next mention of groupoids in a topology text is by S-T Hu, 1964, which defines the fundamental groupoid, as does Spanier, 1966. This led me in the early 1960s to think I ought to include something on groupoids in the book I was writing. Then I came across Philip Higgins' 1964 paper on presentations of groupoids, which included a definition of free products with amalgamation of groupoids; so I set an exercise on a van Kampen type result. When I wrote out a solution of that, it seemed so much better than my then current treatment that I decided to give a full account. It still needed the notion of the fundamental groupoid on a set of base points to get the appropriate general result, published in 1967. My text, now called "Topology and Groupoids", is still the only topology text in English to give a van Kampen theorem in that setting. See the discussion on http://mathoverflow.net/questions/40945/compelling-evidence-that-two-basepoi... In April 1967 G W Mackey introduced himself to me at a British Mathematical Colloquium where I had given a talk on these results, and he told me of his work on virtual groups and ergodic groupoids, which involved the action groupoid of a group action. So I thought I ought to do a chapter on covering spaces using the notion used by Higgins of covering morphism of groupoids. Thus a covering map is modelled algebraically by a covering morphism, which has advantages for results on liftings of maps and morphisms. This fits of course with Reidemeisater's action groupoid, which was used much later by Ehresmann and Grothendieck. The last Chapter of Reidemeister's book is on Branched Coverings. I have often wondered if the use of groupoids can be helpful in that notion. Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]