  This manuscript has two goals: 1. To write an explicit description of the
degenerate residual spectrum of the split, simple, simply-connected,
exceptional groups of type $E_n$ (for $n=6,7,8$). 2. To set a practical guide
for similar calculations and, in particular, to describe various methods of
``computational representation theory'' relevant to the study of residues of
automorphic Eisenstein series.
  In Part I we supply background information and notations from the theory of
automorphic representations as well as concrete information on the exceptional
groups of type $E_n$ and their representation theory over non-Archimedean local
fields.
  In Part II we make a systematic study of the residual spectrum of these
groups where each chapter is devoted to a certain aspect of theory, it begins
with methodical section and continues with sections devoted to the results for
each of these groups.
  We describe completely the residual (square-integrable and non-square
integrable) spectrum of the groups of type $E_6$ and $E_7$ and an almost
complete description in the case of the group of type $E_8$. We also study and
list Siegel-Weil like identities between residual representations of these
groups and list the Arthur parameters for their square-integrable residual
representations.
