This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applications of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cechcohomology is treated in a simple ad hoc fashion for locally compact
subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix.