This is a list of things to add/improve in no particular order. Some topics may have their own article, in which case, a pointer can be added with less information than otherwise would be called for.

• Add a section on reduced homology
• Mention the universal coefficient theorem somewhere appropriate
• Add a table giving (Z-)homology of some common example spaces
  • n-sphere
  • n-torus
  • genus g surface
  • real/complex protective spaces
• Add a properties section including:
  • Excision/Mayer-Vietoris
  • Homology of a disjoint union and of a wedge sum
  • Homology of a suspension
  • Künneth formula
  • Work in the fact that ${\displaystyle H_{0}}$ gives the number of path connected components
  • ...?
• Add a section on the homology of a point as an example
• The way that the singular chain complex is presented needs to be cleaned up significantly
• Equivalence with cellular homology