  We derive, from first principles, the complete Luttinger liquid theory of
abelian quantum Hall edge states. This theory includes the effects of disorder
and Coulomb interactions as well as the coupling to external electromagnetic
fields. We introduce a theory of spatially separated (individually conserved)
edge modes, find an enlarged dual symmetry and obtain a complete classification
of quasiparticle operators and tunneling exponents. The chiral anomaly on the
edge and Laughlin's gauge argument are used to obtain unambiguously the Hall
conductance. In resolving the problem of counter flowing edge modes, we find
that the long range Coulomb interactions play a fundamental role. In order to
set up a theory for arbitrary filling fractions $\nu$ we use the idea of a two
dimensional network of percolating edge modes. We derive an effective, single
mode Luttinger liquid theory for tunneling processes into the quantum Hall edge
which yields a continuous tunneling exponent $1/\nu$. The network approach is
also used to re-derive the instanton vacuum or $Q$-theory for the plateau
transitions.
