[1]:https://web.archive.org/web/20151016170311/http://pages.bangor.ac.uk/~mas010/pdffiles/PROBAMTX.PDF
[2]:https://web.archive.org/web/20151023004804/http://pages.bangor.ac.uk/~mas010/nonab-a-t.html


I have made a note of some problems in the area of [Nonabelian algebraic topology and homological algebra][1] in 1990, and in Chapter 16 of the book in the same area and [advertised here][2], with free pdf,  there is a note of 32 problems and questions in this area which had occurred to me. These problems may well seem "narrow", and/or "out-of-line" of current trends, but I thought  the latter big book ought  not to be seen as any kind of final product, but hopefully as the beginning of a new story. Also it is interesting to record for any area of study what it might be hoped to do but so far does not.  

Further comment: The origin of this work was methodological (does that count as a "problem"?). In  the 1960s, writing  the first edition of the book which is now "Topology and Groupoids" (2006),  I convinced myself that **all of $1$-dimensional homotopy theory** was better expressed in terms of groupoids rather than groups. So the next question was: **are groupoids useful, or not, or to what extent, in higher dimensional homotopy theory?** Trying to find answers to this has been a lot of fun for all concerned, though the 1981 published work with Philip Higgins  was described once to me by Michael Barratt as "Carved out of solid rock, and pursued in the teeth of opposition".