  With analytic applications in mind, in particular Beyond Endoscopy ([13]), we
initiate the study of the elliptic part of the trace formula. Incorporating the
approximate functional equation to the elliptic part we control the analytic
behavior of the volumes of tori that appear in the elliptic part. Furthermore
by carefully choosing the truncation parameter in the approximate functional
equation we smooth-out the singularities of orbital integrals. Finally by an
application of Poisson summation we rewrite the elliptic part so that it is
ready to be used in analytic applications, and in particular in Beyond
Endoscopy. As a by product we also isolate the contributions of special
representations as pointed out in [13].
