  In this article one will develop a new type of energy method based on a
foliation of spacetime into hyperboloidal hypersurfaces . As we will see, with
this method, some classical results such as global existence and almost global
existence of regular solutions to the quasi-linear wave equations and
Klein-Gordon equations will be established in a much simpler and much more
natural way. Most importantly, the global existence of regular solutions to a
general type of coupled quasilinear wave-Klein-Gordon system will be
established. All of this suggests that compared with the classical method, this
hyperboloidal foliation of space-time may be a more natural way to regard the
wave operator.
