I don't see why I should not recommend my own book Topology and Groupoids (T&G) as a text on general topology from a geometric viewpoint and on 1-dimensional homotopy theory from the modern view of groupoids. This allows for a form of the van Kampen theorem with many base points, chosen according to the geometry of the situation, from which one can deduce the fundamental group of the circle, a gap in traditional accounts; also I feel it makes the theory of covering spaces easier to follow since a *covering map* of spaces is modelled by a *covering morphism* of groupoids. Also useful is the notion of **fibration of groupoids**. A further bonus is that there is a theorem on the fundamental groupoid of an orbit space by a discontinuous action of a group, not to be found in any other text, except a 2016 Bourbaki volume in French on "Topologie Algebrique": and that gives no example applications.

The book is available from amazon at $31.99 and a pdf version with hyperref and some colour is available from the web page for the book.

The book has no homology theory, so it contains only one initial part of algebraic topology.

BUT, another part of algebraic topology is in the new jointly authored book Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids (NAT) published in 2011 by the European Mathematical Society. The print version is not cheap, but seems to me good value for 703 pages, and a pdf is available on my web page for the book. Motivation for the methods are given by a thorough presentation of the history and intuitions, and the book should be seen as a sequel to "Topology and Groupoids", to which it refers often.

The new book gives a quite different approach to the border between homotopy and homology, in which there is little singular homology, and no simplicial approximation. Instead, it gives a Higher Homotopy Seifert-van Kampen Theorem, which yields directly results on relative homotopy groups, including nonabelian ones in dimension 2 (!), and including generalisations of the Relative Hurewicz Theorem.

Part I, up to p. 204, is almost entirely on dimension 1 and 2, with lots of figures. You'll find little, if any, of the results on crossed modules in other algebraic topology texts. You will find relevant presentations on my preprint page.

Will this take on? The next 20 years may tell!

October 24, 2016 A new preprint Modelling and Computing Homotopy Types: I is available as an Introduction to the above NAT book. This expands on some material presented at CT2015, the Aveiro meeting on Category Theory.