These notes are an outgrowth of lectures that I delivered
during the spring of 1969 at Aarhus University. They represent
my feeble attempts to organize in a coherent way the circle of
ideas revolving about the spectral sequence introduced by
Eilenberg and Moore in [18], The first part of these notes
presents a new construction for the spectral sequence based on
viewing it as a Kunneth spectral sequence in a suitable category,
the category Top/B of spaces over a fixed space B. This idea
has also been employed by L. Hodgkin whose work has not yet
appeared in print. The category Top/B and its pointed analog
offer a suitable setting for many other ideas, constructions and
theorems. We reccomend that the interested reader consult [8]
[19] [23] [28] [33] and/or [45] for further material in this
direction.