  After a brief review of critical string theory in trivial backgrounds we
begin with introduction to strings in non--trivial backgrounds and noncritical
string theory. In particular, we relate the latter to critical string theory in
a linear dilaton background.
  We then show how a black hole background arises from 2D string theory and
discuss some of its properties. A time--dependant tachyon background is
constructed by perturbing the CFT describing string theory in a linear dilaton
background. It is then explained that the T--dual of this theory with one
non--vanishing tachyon coupling, which is a sine-Liouville CFT, is seemingly
equivalent to the exact CFT describing the Euclidean black hole background.
  Subsequently, we launch into a review of some important facts concerning
random matrix models and matrix quantum mechanics (MQM), culminating in an MQM
model of 2D string theory in a dynamic tachyon background. We then solve this
theory explicitly in the tree level approximation for the case of two
non--vanishing tachyon couplings, which generalises the case of sine-Liouville
CFT previously considered in the literature.
