  We construct two-dimensional non-Abelian topologically ordered states by
strongly coupling arrays of one-dimensional quantum wires via interactions. In
our scheme, all charge degrees of freedom are gapped, so the construction can
use either quantum wires or quantum spin chains as building blocks, with the
same end result. The construction gaps the degrees of freedom in the bulk,
while leaving decoupled states at the edges that are described by conformal
field theories (CFT) in $(1+1)$-dimensional space and time. We consider both
the cases where time-reversal symmetry (TRS) is present or absent. When TRS is
absent, the edge states are chiral and stable. We prescribe, in particular, how
to arrive at all the edge states described by the unitary CFT minimal models
with central charges $c<1$. These non-Abelian spin liquid states have vanishing
quantum Hall conductivities, but non-zero thermal ones. When TRS is present, we
describe scenarios where the bulk state can be a non-Abelian, non-chiral, and
gapped quantum spin liquid, or a gapless one. In the former case, we find that
the edge states are also gapped. The paper provides a brief review of
non-Abelian bosonization and affine current algebras, with the purpose of being
self-contained. To illustrate the methods in a warm-up exercise, we recover the
ten-fold way classification of two-dimensional non-interacting topological
insulators using the Majorana representation that naturally arises within
non-Abelian bosonization. Within this scheme, the classification reduces to
counting the number of null singular values of a mass matrix, with gapless edge
modes present when left and right null eigenvectors exist.
