• "(Counter)examples in Algebraic Topology"

There are many good textbooks in homology and elementary homotopy theory, but the supply of instructive examples they offer is usually appallingly small (spheres and projective spaces are the standard examples, but often there is little beyond). One reason is that to discuss interesting examples, one needs a lot of machinery, whose development consumes time and space. The books by Hatcher or Bredon offer a lot of examples; and I also like Neil Stricklands bestiary:

http://neil-strickland.staff.shef.ac.uk/courses/bestiary/bestiary.pdf,

and together with the unwritten chapter "things left to do", it is pretty close to what I would love to see as a book.

• "(Counter)examples in Algebraic Topology"

There are many good textbooks in homology and elementary homotopy theory, but the supply of instructive examples they offer is usually appallingly small (spheres and projective spaces are the standard examples, but often there is little beyond). One reason is that to discuss interesting examples, one needs a lot of machinery, whose development consumes time and space. The books by Hatcher or Bredon offer a lot of examples; and I also like Neil Stricklands bestiary:

https://strickland1.org/courses/bestiary/bestiary.pdf,

and together with the unwritten chapter "things left to do", it is pretty close to what I would love to see as a book.