Singular homology is usually defined via singular simplices, but Serre in his thesis uses singular cubes, which he claims are better adapted to the study of fibre spaces. This young man (25 years old at the time) seemed to know what he was talking about and has had a not too unsuccessful career since.
So my (quite connected) questions are
1) Why do so few books use this approach ( I only know Massey's) ?
2) What are the pro's and con's of both approaches ?
3) Does it matter ? After all the homology groups obtained are the same.