This monograph developed out of the Abendseminar of 1958-1959
at the University of Zurich. It was originally a joint enterprise of the
first author and H. H. Keller, who planned a brief treatise on connections
in smooth fibre bundles. Then, in 1960, the first author took a position
in the United States and geographic considerations forced the cancellation
of this arrangement.
The collaboration between the first and third authors began with
the former’s move to Toronto in 1962; they were joined by the second
author in 1965. During this time the purpose and scope of the book
grew to its present form: a three-volume study, ab initio, of the de Rham
cohomology of smooth bundles. In particular, the material in volume I
has been used at the University of Toronto as the syllabus for an
introductory graduate course on differentiable manifolds.