  This is a set of lectures on the gauge/string duality and non-critical
strings, with a particular emphasis on the discretized, or matrix model,
approach. After a general discussion of various points of view, I describe the
recent generalization to four dimensional non-critical (or five dimensional
critical) string theories of the matrix model approach. This yields a fully
non-perturbative and explicit definition of string theories with eight (or
more) supercharges that are related to four dimensional CFTs and their relevant
deformations. The space-time as well as world-sheet dimensions of the
supersymmetry preserving world-sheet couplings are obtained. Exact formulas for
the central charge of the space-time supersymmetry algebra as a function of
these couplings are calculated. They include infinite series of string
perturbative contributions as well as all the non-perturbative effects. An
important insight on the gauge theory side is that instantons yield a
non-trivial 1/N expansion at strong coupling, and generate open string
contributions, in addition to the familiar closed strings from Feynman
diagrams. We indicate various open problems and future directions of research.
