  We study topological phases of interacting systems in two spatial dimensions
in the absence of topological order (i.e. with a unique ground state on closed
manifolds and no fractional excitations). These are the closest interacting
analogs of integer Quantum Hall states, topological insulators and
superconductors. We adapt the well-known Chern-Simons {K}-matrix description of
Quantum Hall states to classify such `integer' topological phases. Our main
result is a general formalism that incorporates symmetries into the
{{K}}-matrix description. Remarkably, this simple analysis yields the same list
of topological phases as a recent group cohomology classification, and in
addition provides field theories and explicit edge theories for all these
phases. The bosonic topological phases, which only appear in the presence of
interactions and which remain well defined in the presence of disorder include
(i) bosonic insulators with a Hall conductance quantized to even integers (ii)
a bosonic analog of quantum spin Hall insulators and (iii) a bosonic analog of
a chiral topological superconductor, whose K matrix is the Cartan matrix of Lie
group E$_8$. We also discuss interacting fermion systems where symmetries are
realized in a projective fashion, where we find the present formalism can
handle a wider range of symmetries than a recent group super-cohomology
classification. Lastly we construct microscopic models of these phases from
coupled one-dimensional systems.
