  This note is based on four lectures that I gave at the 10th Taiwan Nuclear
Spring School held at Hualien, Taiwan in January 2002. It aims to correlate the
old notion of Cheshire Cat Principle developed for elementary baryons to the
modern notion of quark-baryon and gluon-meson "continuities" or "dualities" in
dilute and dense many-body systems and predict what would happen to mesons when
squeezed by nuclear matter to high density as possibly realized in compact
stars. Using color-flavor locking in QCD, the vector mesons observed at low
density can be described as the Higgsed gluons dressed by cloud of collective
modes, i.e., pions just as they are in superdense matter, thus showing the
equivalence between hidden $flavor$ gauge symmetry and explicit $color$ gauge
symmetry. Instead of going into details of well-established facts, I focus on a
variety of novel ideas -- some solid and some less -- that could be confirmed
or ruled out in the near future.
