  In this work are consider several topics in the Topological Membrane (TM)
approach to string theory. The string dynamics is generated from the bulk
physics, namely from the 3D Topologically Massive Gauge Theory (TMGT) and
Topologically Massive Gravity (TMG). Both (equivalent) path integral and
canonical methods of quantizing TMGT are studied. It is shown that Narain
constraints on toroidal compactification (integer, even, self-dual momentum
lattice) have a natural interpretation in purely three dimensional terms. The
Heterotic string and the block structure of c=1 RCFT are derived from the point
of view of three dimensional field theory. Open and unoriented strings in
TM(GT) theory are also studied through orbifolds of the bulk 3D space. This is
achieved by gauging discrete symmetries of the theory. Open and unoriented
strings can be obtained from all possible realizations of C, P and T
symmetries. The important role of C symmetry to distinguish between Dirichlet
and Neumann boundary conditions is discussed in detail. Future directions of
research in this field are also suggested and discussed.
