 
Summary: The trace fortmila
THE TRACE FORMULA FOR REDUCTIVE 'GROUPS*
James ARTHUR
This paper is a report on the present state of the trace formula
for a general reductive group. The trace formula is not so much an end
in itself as it is a key to deep results on automorphic representations.
However, such applications have only been carried out for groups of low
dimension (
For reports
groups, see
proceedings
5 1 , 171, [8(c)], [ 3 ] ) . We will not try to discuss them here.
on progress towards applying the trace formula for general
the papers of Langlands [8(d) I and Shelstad [ll] in these
Our discussion will be brief and largely confined to a description
of the main results. On occasion we will try to give some idea of the
proofs, but more often we shall simply refer the reader to papers in the
bibliography. Section 1 will be especially sparse, for it contains a re
view of results which were summarized in more detail in [l(e)].
This report contains no mention of the twisted trace formula.
