Analysis of an old variational principal in classical mechanics has
established global periodic phenomena in Hamiltonian systems. One of the
links is a class of sympletic invariants, called sympletic capacities,
and these invariants are the main theme of this book. Topics covered
include basic sympletic geometry, sympletic capacities and rigidity,
sympletic fixed point theory, and a survey on Floer homology and
sympletic homology.