  We describe some recent progress in understanding and formulating string
theory which is based on extensive studies of strings in lower (D=2) dimension.
At the center is a large $W_{\infty}$ symmetry that appears most simply in the
matrix model picture. In turn the symmetry defines the dynamics giving Ward
identities and the complete S-matrix. The integrability aspect where nonlinear
string phenomena emerges from linear matrix model dynamics is emphasized.
Extensions involving couplings of discrete topological fields to the tachyon
are also described.
