  We propose a unifying model for FQHE which on the one hand connects it to
recent developments in string theory and on the other hand leads to new
predictions for the principal series of experimentally observed FQH systems
with filling fraction $\nu ={n\over 2n\pm1}$ as well as those with $\nu
={m\over m+2}$. Our model relates these series to minimal unitary models of the
Virasoro and superVirasoro algebra and is based on $SL(2, {\bf C})$
Chern-Simons theory in Euclidean space or $SL(2,{\bf R})\times SL(2,{\bf R})$
Chern-Simons theory in Minkowski space. This theory, which has also been
proposed as a soluble model for 2+1 dimensional quantum gravity, and its N=1
supersymmetric cousin, provide effective descriptions of FQHE. The principal
series corresponds to quantized levels for the two $SL(2,{\bf R})$'s such that
the diagonal $SL(2,{\bf R})$ has level $ 1$. The model predicts, contrary to
standard lore, that for principal series of FQH systems the quasiholes possess
non-abelian statistics. For the multi-layer case we propose that complex ADE
Chern-Simons theories provide effective descriptions, where the rank of the ADE
is mapped to the number of layers. Six dimensional $(2,0)$ ADE theories on the
Riemann surface $\Sigma$ provides a realization of FQH systems in M-theory.
Moreover we propose that the q-deformed version of Chern-Simons theories are
related to the anisotropic limit of FQH systems which splits the zeroes of the
Laughlin wave function. Extensions of the model to 3+1 dimensions, which
realize topological insulators with non-abelian topologically twisted
Yang-Mills theory is pointed out.
