This advertises Part I of a three part book with the above title. We are putting Part I (with overall TOC) on the web to awake interest and in the hope of getting comments and suggestions. Details are on http://www.bangor.ac.uk/~mas010/nonab-a-t.html Special interest for this list should be the use of higher categorical structures. Ronnie Brown and Rafael Sivera Villenueva Professor Emeritus R. Brown, Department of Mathematics, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Centre for the Popularisation of Mathematics: http://www.cpm.informatics.bangor.ac.uk/ (reorganised site with new sculpture animations)