The action of a compact Lie group, G, on a compact sympletic manifold gives rise
to some remarkable combinatorial invariants. The simplest and most interesting
of these is the moment polytopes, a convex polyhedron which sits inside the dual
of the Lie algebra of G. One of the main goals of this monograph is to describe
what kinds of geometric information are encoded in this polytope. This book is
addressed to researchers and can be used as a semester text.