  Beginning with the basic notions of quantum theory, impossibility of
`trajectory' description for particles that ensues from uncertainty principle
is discussed. Why the observed tracks in bubble/cloud chambers are not really
the `trajectories' of high energy particles, rather they are simply the trails
of the atoms/molecules excited or ionized in the direction of the high momenta
of the incoming particles, are highlighted. Thereafter, the notion of symmetry
and its application to the non-relativistic Schrodinger equation have been
delineated. The demand for U(1) gauge invariance and the resulting `gauge
miracle', that automatically leads to the correct interaction terms describing
the electromagnetic force between the charge particles and the field, have been
elaborated upon. A simple treatment, but with explicit derivation, of the
Aharonov-Bohm effect, is presented, that underlines a strange phenomena -
sites, impenetrable by charge particles but are threaded with magnetic field
lines, conspire with a `Trojan Horse', namely the magnetic vector potential
outside, to cause measurable shift in the double-slit interference fringes.
This shift in the interference pattern is non-classical since the charge
particles move in field-free regions. The crucial Aharonov-Bohm (AB) phase that
makes its entry in the above bizarre effect is also deployed to derive the
observed magnetic flux quantisation in superconductors as well as the Dirac
result which implies that the existence of a single magnetic monopole anywhere
in the universe would entail quantisation of the product of a particle's
electric charge and the monopole's magnetic charge. Nontrivial consequences of
AB phase follow whenever the physical region accessible, from the point of view
of the wavefunction of a charge particle, is multiply-connected.
