  In these lecture notes, we present a self-contained discussion of planar
gauge theories broken down to some finite residual gauge group H via the Higgs
mechanism. The main focus is on the discrete H gauge theory describing the long
distance physics of such a model. The spectrum features global H charges,
magnetic vortices and dyonic combinations. Due to the Aharonov-Bohm effect,
these particles exhibit topological interactions. Among other things, we review
the Hopf algebra related to this discrete H gauge theory, which provides an
unified description of the spin, braid and fusion properties of the particles
in this model. Exotic phenomena such as flux metamorphosis, Alice fluxes,
Cheshire charge, (non)abelian braid statistics, the generalized spin-statistics
connection and nonabelian Aharonov-Bohm scattering are explained and
illustrated by representative examples.
  Preface: Broken symmetry revisited,
  1 Basics: 1.1 Introduction, 1.2 Braid groups, 1.3 Z_N gauge theory, 1.3.1
Coulomb screening, 1.3.2 Survival of the Aharonov-Bohm effect, 1.3.3 Braid and
fusion properties of the spectrum, 1.4 Nonabelian discrete gauge theories,
1.4.1 Classification of stable magnetic vortices, 1.4.2 Flux metamorphosis,
1.4.3 Including matter,
  2 Algebraic structure: 2.1 Quantum double, 2.2 Truncated braid groups, 2.3
Fusion, spin, braid statistics and all that...,
  3 \bar{D}_2 gauge theory: 3.1 Alice in physics, 3.2 Scattering doublet
charges off Alice fluxes, 3.3 Nonabelian braid statistics, 3.A Aharonov-Bohm
scattering, 3.B B(3,4) and P(3,4),
  Concluding remarks and outlook
