  In this paper, applying a canonical system with field rotation parameters and
using geometric properties of the spirals filling the interior and exterior
domains of limit cycles, we solve first the problem on the maximum number of
limit cycles surrounding a unique singular point for an arbitrary polynomial
system. Then, by means of the same bifurcationally geometric approach, we solve
the limit cycle problem for a general Li\'enard polynomial system with an
arbitrary (but finite) number of singular points. This is related to the
solution of Hilbert's sixteenth problem on the maximum number and relative
position of limit cycles for planar polynomial dynamical systems.
