This volume grew out of a series of preprints which were written and
circulated - tween 1993 and 1994. Around the same time, related work was
done independently by Harder [40] and Laumon [62]. In writing this
text based on a revised version of these preprints that were widely
distributed in summer 1995, I ?nally did not p- sue the original plan to
completely reorganize the original preprints. After the long delay, one
of the reasons was that an overview of the results is now available in
[115]. Instead I tried to improve the presentation modestly, in
particular by adding cross-references wherever I felt this was
necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5
were added; these were written in 1998. I willgivea
moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that
I should mention that the two main results are the proof of Ramanujan's
conjecture for Siegel modular forms of genus 2 for forms which are not
cuspidal representations associated with parabolic subgroups(CAP
representations), and the study of the endoscopic lift for the group
GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters
assuming the stabilization of the trace formula. All the remaining
technical results, which are necessary to obtain the stabilized trace
formula, are presented in the remaining chapters. Chapter 1 gathers
results on the cohomology of Siegel modular threefolds that are used in
later chapters, notably in Chap. 3. At the beginning of Chap.
